Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 142, no. 9, 2012]]>

For attribute data with (very) small failure rates control charts were introduced which are based on subsequent groups of r failure times, for some r >= 1. Within this family, it was shown to be attractive to stop once the maximum of such a group is sufficiently small, because this choice allows a very satisfactory nonparametric adaptation. The question we ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, pp. 1924-1932, 2012]]>In a latin square of order n, a k-plex is a selection of kn entries in which each row, column and symbol occurs k times. A 1-plex is also called a transversal. An indivisible k-plex is one that contains no c-plex for 0ck. For orders n∉{2,6}, existence of latin squares with a partition into ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 402-417, 2011]]>This paper is concerned with the pile-up model defined as a nonlinear transformation of a distribution of interest. An observation of the pile-up model is the minimum of a random number of independent variables from the distribution of interest. One specific pile-up model is encountered in time-resolved fluorescence where only the first photon of a random ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 1-16, 2011]]>Ranked-set sampling (RSS) and judgment post-stratification (JPS) use ranking information to obtain more efficient inference than is possible using simple random sampling. Both methods were developed with subjective, judgment-based rankings in mind, but the idea of ranking using a covariate has received a lot of attention. We provide evidence here that when rankings are done using a ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 2, pp. 809-816, 2011]]>In this paper, we investigate the maximum likelihood estimation for the reflected Ornstein–Uhlenbeck (ROU) processes based on continuous observations. Both the cases with one-sided barrier and two-sided barriers are considered. We derive the explicit formulas for the estimators, and then prove their strong consistency and asymptotic normality. Moreover, the bias and mean square errors are represented in ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 588-596, 2011]]>A spline-backfitted kernel smoothing method is proposed for partially linear additive model. Under assumptions of stationarity and geometric mixing, the proposed function and parameter estimators are oracally efficient and fast to compute. Such superior properties are achieved by applying to the data spline smoothing and kernel smoothing consecutively. Simulation experiments with both moderate and large number of variables confirm ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 204-219, 2011]]>Open label and single blinded randomized controlled clinical trials are vulnerable to selection bias when the next treatment assignment is predictable based on the randomization algorithm and the preceding assignment history. While treatment predictability is an issue for all constrained randomization algorithms, deterministic assignments are unique to permuted block randomization. Deterministic assignments may lead to treatment predictability with certainty and ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 474-478, 2011]]>The maximum likelihood estimator (MLE) is asymptotically efficient for most parametric models under standard regularity conditions, but it has very poor robustness properties. On the other hand some of the minimum disparity estimators like the minimum Hellinger distance estimator (MHDE) have strong robustness features but their small sample efficiency at the model turns out to be very poor compared to ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 2, pp. 701-710, 2011]]>In this paper D- and V-optimal population designs for the quadratic regression model with a random intercept term and with values of the explanatory variable taken from a set of equally spaced, non-repeated time points are considered. D-optimal population designs based on single-point individual designs were readily found but the derivation of explicit expressions for designs ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 2, pp. 889-898, 2011]]>The estimation of a linear combination of several restricted location parameters is addressed from a decision-theoretic point of view. Although the corresponding linear combination of the unbiased estimators is minimax under the restricted problem, it has a drawback of taking values outside the restricted parameter space. Thus, it is reasonable to use the linear combination of the restricted estimators ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 6, pp. 2141-2155, 2011]]>We establish a reflection principle for three lattice walkers and use this principle to reduce the enumeration of configurations of three vicious walkers to the enumeration of configurations of two vicious walkers. More precisely, the reflection principle leads to a bijection between three walks (L1, L2, L3) such that L2 intersects both L1 and L3 and three walks (L1, L2, ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 94-101, 2011]]>In this paper, we mainly aim to introduce the notion of improved Liu estimator (ILE) in the linear regression model y=Xβ+e. The selection of the biasing parameters is investigated under the PRESS criterion and the optimal selection is successfully derived. We make a simulation study to show the performance of ILE compared to the ordinary least squares estimator and ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 189-196, 2011]]>In this paper we propose a smooth test of comparison of two distribution functions. This test adapts to the classical two-sample problem as well as that of paired populations, including discrete distributions. A simulation study and an application to real data show its good performances.

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 262-275, 2011]]>This paper deals with the classical problem of density estimation on the real line. Most of the existing papers devoted to minimax properties assume that the support of the underlying density is bounded and known. But this assumption may be very difficult to handle in practice. In this work, we show that, exactly as a curse of dimensionality exists when ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 115-139, 2011]]>A two-phase approach for sampling with unequal inclusions probabilities and fixed sample size is presented. The expansion estimator using target inclusion probabilities is suggested for estimation of population parameters. As an alternative, the estimator for two-phase sampling can be used for estimation. Inclusion probabilities are shown to be asymptotically equivalent to the targeted inclusion probabilities. By means of ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 5, pp. 1646-1654, 2011]]>This paper introduces a new class of time-varying, measure-valued stochastic processes for Bayesian nonparametric inference. The class of priors is constructed by normalising a stochastic process derived from non-Gaussian Ornstein–Uhlenbeck processes and generalises the class of normalised random measures with independent increments from static problems. Some properties of the normalised measure are investigated. A particle filter ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 11, pp. 3648-3664, 2011]]>In a Type-II right censored sample from the standard uniform distribution, several transformations of respective order statistics are examined, which transform the censored sample into a complete sample in a lower dimension. Such transformations have been considered by Lin et al. (2008), Michael and Schucany (1979) and O’Reilly and Stephens (1988) in the context of goodness-of-fit tests. ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 536-548, 2011]]>Orthogonal and partly orthogonal reparametrisations are provided for certain wide and important families of univariate continuous distributions. First, the orthogonality of parameters in location-scale symmetric families is extended to symmetric distributions involving a third parameter. This sets the scene for consideration of the four-parameter situation in which skewness is also allowed. It turns out that one specific approach ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 2, pp. 758-770, 2011]]>This paper studies nonparametric regression with long memory (LRD) errors and predictors. First, we formulate general conditions which guarantee the standard rate of convergence for a nonparametric kernel estimator. Second, we calculate the mean integrated squared error (MISE). In particular, we show that LRD of errors may influence MISE. On the other hand, an estimator for a shape function is ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 508-523, 2011]]>In this paper, we investigate ordering properties of lifetimes of parallel systems with two independent heterogeneous exponential components in terms of the mean residual life order. We establish, among others, that the reciprocal majorization order between parameter vectors implies the mean residual life order between the lifetimes of two parallel systems. We then extend this result to the proportional hazard ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 2, pp. 631-638, 2011]]>The paper concerns the design of nonparametric low-pass filters that have the property of reproducing a polynomial of a given degree. Two approaches are considered. The first is locally weighted polynomial regression (LWPR), which leads to linear filters depending on three parameters: the bandwidth, the order of the fitting polynomial, and the kernel. We find a remarkable linear (hyperbolic) ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 2, pp. 831-845, 2011]]>Two sufficient conditions for comparing convolutions of heterogeneous gamma random variables in terms of star order are established. It is further shown that if the scale parameters of heterogeneous gamma random variables are more dispersed in the sense of majorization, then the convolutions are more dispersed according to the right spread order, which generalizes and strengthens the results in Diaconis ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 418-428, 2011]]>Optimal k-circulant supersaturated designs have been constructed in literature using computer intensive methods. A systematic method of construction for multi-level experiments based on balanced incomplete block designs is presented in this paper. The method is also applicable to two-level experiments. Illustrative examples are also given.

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 2, pp. 782-786, 2011]]>We have considered the functional linear model with scalar response and functional explanatory variable. One of the most popular methodologies for estimating the model parameter is based on functional principal components analysis (FPCA). In recent literature, weak convergence for a wide class of FPCA-type estimates has been proved, and consequently asymptotic confidence sets can be built. In this paper, ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 453-461, 2011]]>This article presents a simplified means of controlling the experiment-wise risk of declaring too many effects active when analyzing an unreplicated orthogonal design. The method begins by assuming a lower bound on the number of null effects. The regression method of backward elimination is followed, comparing each F statistic with a common critical value, until the first statistically significant ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 325-334, 2011]]>Progressive multi-state models provide a convenient framework for characterizing chronic disease processes where the states represent the degree of damage resulting from the disease. Incomplete data often arise in studies of such processes, and standard methods of analysis can lead to biased parameter estimates when observation of data is response-dependent. This paper describes a joint analysis useful for ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 80-93, 2011]]>Several omnibus tests of the proportional hazards assumption have been proposed in the literature. In the two-sample case, tests have also been developed against ordered alternatives like monotone hazard ratio and monotone ratio of cumulative hazards. Here we propose a natural extension of these partial orders to the case of continuous and potentially time varying covariates, and develop tests ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 243-261, 2011]]>Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 610-610, 2011]]>

This paper explores the use of data augmentation in settings beyond the standard Bayesian one. In particular, we show that, after proposing an appropriate generalised data-augmentation principle, it is possible to extend the range of sampling situations in which fiducial methods can be applied by constructing Markov chains whose stationary distributions represent valid posterior inferences on model parameters. Some ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 156-171, 2011]]>Independent random variables Xλ1,…,Xλn are said to belong to the scale family of distributions if Xλi∼F(λix), for i=1,…,n, where F is an absolutely continuous distribution function with hazard rate r and reverse hazard rate r˜. We show that the hazard rate (reverse hazard rate) of a series (parallel) system consisting of components with lifetimes ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 276-286, 2011]]>Deterministic computer simulations are often used as replacement for complex physical experiments. Although less expensive than physical experimentation, computer codes can still be time-consuming to run. An effective strategy for exploring the response surface of the deterministic simulator is the use of an approximation to the computer code, such as a Gaussian process (GP) model, coupled with a sequential ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 42-55, 2011]]>Panel data with covariate measurement error appear frequently in various studies. Due to the sampling design and/or missing data, panel data are often unbalanced in the sense that panels have different sizes. For balanced panel data (i.e., panels having the same size), there exists a generalized method of moments (GMM) approach for adjusting covariate measurement error, which does ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 2, pp. 800-808, 2011]]>There is much literature on statistical inference for distribution under missing data, but surprisingly very little previous attention has been paid to missing data in the context of estimating distribution with auxiliary information. In this article, the auxiliary information with missing data is proposed. We use Zhou, Wan and Wang's method (2008) to mitigate the effects of missing data ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 2, pp. 711-724, 2011]]>The use of lower probabilities is considered for inferences in basic jury scenarios to study aspects of the size of juries and their composition if society consists of subpopulations. The use of lower probability seems natural in law, as it leads to robust inference in the sense of providing a defendant with the benefit of the doubt. The method presented ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 382-391, 2011]]>Crossover designs, or repeated measurements designs, are used for experiments in which t treatments are applied to each of n experimental units successively over p time periods. Such experiments are widely used in areas such as clinical trials, experimental psychology and agricultural field trials. In addition to the direct effect on the response of the treatment in the period of ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 2, pp. 846-860, 2011]]>In this paper the work of Pancheva (1984) for extreme order statistics under nonlinear normalization is extended to order statistics with variable ranks. Two new results are proved. The first is that under nonlinear normalization, the nondegenerate type (family of types) of the distribution functions with two finite growth points is a possible weak limit of any central order statistic ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 524-535, 2011]]>In mixture experiments the properties of mixtures are usually studied by mixing the amounts of the mixture components that are required to obtain the necessary proportions. This paper considers the impact of inaccuracies in discharging the required amounts of the mixture components on the statistical analysis of the data. It shows how the regression calibration approach can be used to ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 2, pp. 692-700, 2011]]>We consider estimation of a class of power-transformed threshold GARCH models. When the power of the transformation is known, the asymptotic properties of the quasi-maximum likelihood estimator (QMLE) are established under mild conditions. Two sequences of least-squares estimators are also considered in the pure ARCH case, and it is shown that they can be asymptotically more accurate ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 488-507, 2011]]>In many toxicological assays, interactions between primary and secondary effects may cause a downturn in mean responses at high doses. In this situation, the typical monotonicity assumption is invalid and may be quite misleading. Prior literature addresses the analysis of response functions with a downturn, but so far as we know, this paper initiates the study of experimental design for ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 559-575, 2011]]>A D-optimal minimax design criterion is proposed to construct two-level fractional factorial designs, which can be used to estimate a linear model with main effects and some specified interactions. D-optimal minimax designs are robust against model misspecification and have small biases if the linear model contains more interaction terms. When the D-optimal minimax criterion is compared ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 576-587, 2011]]>There are several ways to select units with replacement and an equal inclusion expectation. We present a new sampling design called simple random sampling with over-replacement. Its interest lies in the high variance produced for the Horvitz–Thompson estimator. This characteristic could be useful for resampling methods.

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 597-601, 2011]]>We analyze the rate of convergence of the estimation error in regularized least-squares regression when the data is exponentially beta-mixing. The results are proven under the assumption that the metric entropy of the balls in the chosen function space grows at most polynomially. In order to prove our main result, we also derive a relative deviation concentration inequality ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 142, pp. 493-505, 2011]]>Local depth is a generalization of ordinary depth able to reveal local features of the probability distribution. Liu's simplicial depth is primarily used, but results for Tukey's halfspace depth are also derived. It is shown that the maximizers of local depth can help to detect the mode(s) of a probability distribution. This work is devoted to the ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 2, pp. 817-830, 2011]]>Estimation of a regression function from independent and identical distributed data is considered. The L2 error with integration with respect to the design measure is used as error criterion. Upper bounds on the L2 error of least squares regression estimates are presented, which bound the error of the estimate in case that in the sample given to the estimate the ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 172-188, 2011]]>Zhang et al. (2008) introduced an aliased effect-number pattern (AENP) for two-level regular designs and proposed a general minimum lower-order confounding (GMC) criterion for choosing optimal designs. By using a finite projective geometric formulation, Zhang and Mukerjee (2009a) characterized GMC designs via complementary designs for general s-level case, and to find GMC designs, for some special ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 5, pp. 1774-1782, 2011]]>In this paper, we derive explicit computable expressions for the asymptotic distribution of the maximum likelihood estimate of an unknown change-point in a sequence of independently and exponentially distributed random variables. First we state and prove a theorem that shows asymptotic equivalence of the change-point mle for the cases of both known and unknown parameters, respectively. Thereafter, the ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 220-234, 2011]]>This article proposes an adjusted empirical likelihood estimation (AMELE) method to model and analyze accelerated life testing data. This approach flexibly and rigorously incorporates distribution assumptions and regression structures by estimating equations within a semiparametric estimation framework. An efficient method is provided to compute the empirical likelihood estimates, and asymptotic properties are studied. Real-life examples and numerical studies demonstrate ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 140-155, 2011]]>For comparing treatments in clinical trials, Atkinson (1982) introduced optimal biased coins for balancing patients across treatment assignments by using D-optimality under the assumption of homoscedastic responses of different treatments. However, this assumption can be violated in many real applications. In this paper, we relax the homoscedasticity assumption in the k treatments setting with k>2. A general ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 235-242, 2011]]>In the cases with three ordinal diagnostic groups, the important measures of diagnostic accuracy are the volume under surface (VUS) and the partial volume under surface (PVUS) which are the extended forms of the area under curve (AUC) and the partial area under curve (PAUC). This article addresses confidence interval estimation of the difference in paired VUS s and the ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 549-558, 2011]]>We show that the asymptotic mean of the log-likelihood ratio in a misspecified model is a differential geometric quantity that is related to the exponential curvature of Efron (1978), Amari (1982), and the preferred point geometry of Critchley et al. (1993, 1994). The mean is invariant with respect to reparameterization, which leads to the differential geometrical approach where coordinate-...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 6, pp. 2091-2099, 2011]]>In statistical and econometric practice it is not uncommon to find that regression parameter estimates obtained using estimated generalized least squares (EGLS) do not differ much from those obtained through ordinary least squares (OLS), even when the assumption of spherical errors is violated. To investigate if one could ignore non-spherical errors, and legitimately continue with OLS estimation under the ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 293-304, 2011]]>We examine a more general form of consistency which does not necessarily rely on the correct specification of the likelihood in the Bayesian setting, but we restrict the form of the likelihood to be in a minimal standard exponential family. First, we investigate the asymptotic behavior of the Bayes estimator of a parameter, and show that the Bayes estimator is ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 2, pp. 748-757, 2011]]>Calibration methods have been widely studied in survey sampling over the last decades. Viewing calibration as an inverse problem, we extend the calibration technique by using a maximum entropy method. Finding the optimal weights is achieved by considering random weights and looking for a discrete distribution which maximizes an entropy under the calibration constraint. This method points a new frame ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 305-317, 2011]]>In this paper, we establish several recurrence relations for the single and product moments of progressively Type-II right censored order statistics from a logistic distribution. The use of these relations in a systematic manner allows us to compute all the means, variances and covariances of progressively Type-II right censored order statistics from the logistic distribution for all sample ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 17-30, 2011]]>The aim of this paper is to study both the pointwise and uniform consistencies of the kernel regression estimate and to derive also rates of convergence whenever functional stationary ergodic data are considered. More precisely, in the ergodic data setting, we consider the regression of a real random variable Y over an explanatory random variable X taking values in some ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 359-372, 2011]]>Existence and consistency of the Maximum Likelihood estimator of the parameters of heterogeneous mixtures of Gaussian and uniform distributions with known number of components are shown under constraints to prevent the likelihood from degeneration and to ensure identifiability. The EM-algorithm is discussed, and for the special case with a single uniform component a practical scheme to find a good ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 462-473, 2011]]>Kunert and Martin (2000) determined optimal and efficient block designs in a model for field trials with interference effects, for block sizes up to 4. The present paper uses Kushner's (1997) method of finding optimal approximate designs to extend the work of Kunert and Martin (2000) to optimal designs with five or more plots per block. We give an ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 4, pp. 1623-1632, 2011]]>Many methods based on ranked set sampling (RSS) assume perfect ranking of the samples. Here, by using the data measured by a balanced RSS scheme, we propose a nonparametric test for the assumption of perfect ranking. The test statistic that we use formally corresponds to the Jonckheere–Terpstra-type test statistic. We show formal relations of the proposed test for ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 2, pp. 624-630, 2011]]>Statistical agencies have conflicting obligations to protect confidential information provided by respondents to surveys or censuses and to make data available for research and planning activities. When the microdata themselves are to be released, in order to achieve these conflicting objectives, statistical agencies apply statistical disclosure limitation (SDL) methods to the data, such as noise addition, swapping or microaggregation. Some ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 31-41, 2011]]>After initiating the theory of optimal design by Smith (1918), many optimality criteria were introduced. Atkinson et al. (2007) used the definition of compound design criteria to combine two optimality criteria and introduced the DT- and CD-optimalities criteria. This paper introduces the CDT-optimum design that provides a specified balance between model discrimination, parameter estimation and estimation of a ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 2, pp. 639-643, 2011]]>We consider nonparametric estimation of a regression curve when the data are observed with Berkson errors or with a mixture of classical and Berkson errors. In this context, other existing nonparametric procedures can either estimate the regression curve consistently on a very small interval or require complicated inversion of an estimator of the Fourier transform of a nonparametric regression estimator. ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 102-114, 2011]]>The Wilcoxon–Mann–Whitney statistic is commonly used for a distribution-free comparison of two groups. One requirement for its use is that the sample sizes of the two groups are fixed. This is violated in some of the applications such as medical imaging studies and diagnostic marker studies; in the former, the violation occurs since the number of correctly ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 335-344, 2011]]>In this paper, we study the construction of confidence intervals for a probability density function under a negatively associated sample by using the blockwise technique. It is shown that the blockwise empirical likelihood (EL) ratio statistic is asymptotically χ2‐type distributed. The result is used to obtain EL based confidence interval on the probability density function.

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 373-381, 2011]]>This paper extends the limiting results of West and Harrison (1997, section 5.5) about the convergence of the variances of time series dynamic linear models (TSDLMs) when both, the variances of the observation and evolution errors of the model, are time-varying with steady limits. Analytical results are derived and an illustrative example is provided.

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 602-609, 2011]]>In this paper, we propose to include Weibull tail-distributions in a more general family of distributions. In particular, the considered model also encompasses the whole Fréchet maximum domain of attraction as well as log-Weibull tail-distributions. The asymptotic normality of some tail estimators based on the log-spacings between the largest order statistics is established in a unified...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 429-444, 2011]]>This paper deals with the problem of estimating the Pearson correlation coefficient when one variable is subject to left or right censoring. In parallel to the classical results on the Pearson correlation coefficient, we derive a workable formula, through tedious computation and intensive simplification, of the asymptotic variances of the maximum likelihood estimators in two cases: (1) known means and ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 392-401, 2011]]>Generalized degrees of freedom measure the complexity of a modeling procedure; a modeling procedure is a combination of model selection and model fitting. In this manuscript, we consider two definitions of generalized degrees of freedom for a modeling procedure under the L1 loss function, and investigate the connections between those two definitions. We also propose the extended Akaike information criterion, ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 2, pp. 677-686, 2011]]>In this paper, a new lower bound to A2-optimality measure is derived and is applied to multi-level and mixed-level column balanced designs. A2-optimal multi-level and mixed-level designs are obtained by the application of the new lower bound.

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 2, pp. 877-888, 2011]]>The cube method proposed by Deville and Tillé (2004) enables the selection of balanced samples: that is, samples such that the Horvitz–Thompson estimators of auxiliary variables match the known totals of those variables. As an exact balanced sampling design often does not exist, the cube method generally proceeds in two steps: a “flight phase” in which exact balance is...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 479-487, 2011]]>Linear models with a growing number of parameters have been widely used in modern statistics. One important problem about this kind of model is the variable selection issue. Bayesian approaches, which provide a stochastic search of informative variables, have gained popularity. In this paper, we will study the asymptotic properties related to Bayesian model selection when the model dimension p ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 11, pp. 3463-3474, 2011]]>Decision making with adaptive utility provides a generalisation to classical Bayesian decision theory, allowing the creation of a normative theory for decision selection when preferences are initially uncertain. In this paper we address some of the foundational issues of adaptive utility as seen from the perspective of a Bayesian statistician. The implications that such a generalisation has upon the traditional ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 2, pp. 734-747, 2011]]>The performance of a treatment is affected by the treatments applied to its adjacent plots, especially in the experiments of agriculture, horticulture, forestry, serology and industry. Neighbor designs ensure that treatment comparisons are least affected by neighbor effects, therefore, this is a rich field of investigation in statistics and in combinatorics. In this article, several series of neighbor balanced designs ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 2, pp. 687-691, 2011]]>Most growth curves can only be used to model the tumor growth under no intervention. To model the growth curves for treated tumor, both the growth delay due to the treatment and the regrowth of the tumor after the treatment need to be taken into account. In this paper, we consider two tumor regrowth models and determine the locally D- ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 2, pp. 644-654, 2011]]>The consistency of estimators in finite mixture models has been discussed under the topology of the quotient space obtained by collapsing the true parameter set into a single point. In this paper, we extend the results of Cheng and Liu (2001) to give conditions under which the maximum likelihood estimator (MLE) is strongly consistent in such a sense in finite ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 56-64, 2011]]>In this paper, we argue that replacing the expectation of the loss in statistical decision theory with the median of the loss leads to a viable and useful alternative to conventional risk minimization particularly because it can be used with heavy tailed distributions. We investigate three possible definitions for such medloss estimators and derive examples of them in several standard ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 2, pp. 611-623, 2011]]>We characterize joint tails and tail dependence for a class of stochastic volatility processes. We derive the exact joint tail shape of multivariate stochastic volatility with innovations that have a regularly varying distribution tail. This is used to give four new characterizations of tail dependence. In three cases tail dependence is a non-trivial function of linear volatility memory parametrically ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 2, pp. 663-676, 2011]]>Sun [2006, The Bahadur representation for sample quantiles under weak dependence. Statist. Probab. Lett. 76, 1238–1244] established the Bahadur representation for sample quantiles under the strongly mixing sequence. But there are some problems in the proofs of the main results. In the paper, we further investigate the Bahadur representation for sample quantiles under strongly mixing sequence and get better ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 2, pp. 655-662, 2011]]>We consider portmanteau tests for testing the adequacy of structural vector autoregressive moving-average (VARMA) models under the assumption that the errors are uncorrelated but not necessarily independent. The structural forms are mainly used in econometrics to introduce instantaneous relationships between economic variables. We first study the joint distribution of the quasi-maximum likelihood estimator (QMLE) and the noise empirical ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 8, pp. 2961-2975, 2011]]>This paper discusses a class of tests of lack-of-fit of a parametric regression model when design is non-random and uniform on [0,1]. These tests are based on certain minimized distances between a nonparametric regression function estimator and the parametric model being fitted. We investigate asymptotic null distributions of the proposed tests, their consistency and asymptotic power ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 65-79, 2011]]>It is shown that the commonly used Weibull-Gamma frailty model has a finite number of finite moments only and that its marginal distribution generalizes the log-logistic distribution. In some cases there is not even a finite variance, and there are cases without a single finite moment. Upon transformation to the entire real line, generalized logistic and generalized Cauchy ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 2, pp. 861-868, 2011]]>Spline smoothing is a popular technique for curve fitting, in which selection of the smoothing parameter is crucial. Many methods such as Mallows’ Cp, generalized maximum likelihood (GML), and the extended exponential (EE) criterion have been proposed to select this parameter. Although Cp is shown to be asymptotically optimal, it is usually outperformed by other selection criteria for small to ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 445-452, 2011]]>Failure time data subject to three progressive Type-I multistage censoring schemes are studied. Product limit estimators are proposed for the estimation of the survival function. It is shown that the resulting estimators are asymptotically equivalent to the corresponding estimators where the data are subject to a random iid right censoring scheme. Many well-known results on confidence bands and ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 2, pp. 910-923, 2011]]>It is often assumed in statistics that the random variables under consideration come from a continuous distribution. However, real data is always given in a rounded (discretized) form. The rounding errors become serious when the sample size is large. In this paper, we consider the situation where the mesh of discretization tends to zero as the sample size tends to ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 287-292, 2011]]>This paper addresses the problem of estimating the mode of a density function based on contaminated data. Unlike conventional methods, which are based on localizing the maximum of a density estimator, we introduce a procedure which requires computation of the maximum among finitely many quantities only. We show that our estimator is strongly consistent under very weak conditions, where not ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 2, pp. 771-781, 2011]]>We investigate the posterior rate of convergence for wavelet shrinkage using a Bayesian approach in general Besov spaces. Instead of studying the Bayesian estimator related to a particular loss function, we focus on the posterior distribution itself from a nonparametric Bayesian asymptotics point of view and study its rate of convergence. We obtain the same rate as in Abramovich et ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 318-324, 2011]]>In this paper we study circular consecutive k-out-of-n systems consisting of exchangeable components. We derive explicit expressions for both unconditional and conditional survival functions for 2k+1≥n, while signature based mixture representations for general k are obtained. The applications and computational results concerned with mean residual life function and stochastic ordering are presented.

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 2, pp. 725-733, 2011]]>We derive an explicit, closed form expression for the double generating function of the corresponding counts of occurrence, within a finite time horizon, of the single patterns contained in a compound pattern. The expression is in terms of a basic single, and a basic joint, generating functions for which exact solutions exist in the literature. The single generating function is ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 7, pp. 2298-2302, 2011]]>We consider statistical inference for partially linear single-index models (PLSIM) when some linear covariates are not observed, but ancillary variables are available. Based on the profile least-squared estimators of the unknowns, we study the testing problems for parametric components in the proposed models. It is to see whether the generalized likelihood ratio (GLR) tests proposed by Fan et ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 2, pp. 899-909, 2011]]>This article introduces a parametric robust way of determining the mean–variance relationship in the setting of generalized linear models. More specifically, the normal likelihood is properly amended to become asymptotically valid even if normality fails. Consequently, legitimate inference for the parametric relationship between mean and variance could be derived under model misspecification. More details are given to the scenario ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 197-203, 2011]]>We investigate the performance of linearly penalized likelihood estimators for estimating distributional parameters in the presence of data truncation. Truncation distorts the likelihood surface to create instabilities and high variance in the estimation of these parameters, and the penalty terms help in many cases to decrease estimation error and increase robustness. Approximate methods are provided for choosing a priori good ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 1, pp. 345-358, 2011]]>In the paper, we consider a linear mixed model (LMM) for longitudinal data under linear restriction and find the estimators for the parameters of interest. The strong consistency and asymptotic normality of the estimators are obtained under some regularity conditions. Besides, we derive the strong consistent estimator of the fourth moment for the error which is useful for statistical inference ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 2, pp. 869-876, 2011]]>For attribute data with (very) small failure rates often control charts are used which decide whether to stop or to continue each time r failures have occurred, for some r⩾1. Because of the small probabilities involved, such charts are very sensitive to estimation effects. This is true in particular if the underlying failure rate varies and hence the distributions involved ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 9, pp. 3151-3159, 2011]]>The main object of Bayesian statistical inference is the determination of posterior distributions. Sometimes these laws are given for quantities devoid of empirical value. This serious drawback vanishes when one confines oneself to considering a finite horizon framework. However, assuming infinite exchangeability gives rise to fairly tractable a posteriori quantities, which is very attractive in applications. Hence, with a view ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 141, no. 2, pp. 787-799, 2011]]>Computer models are widely used in scientific research to study and predict the behaviour of complex systems. The run times of computer-intensive simulators are often such that it is impractical to make the thousands of model runs that are conventionally required for sensitivity analysis, uncertainty analysis or calibration. In response to this problem, highly efficient techniques have recently been ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 140, no. 3, pp. 640-651, 2010]]>This paper investigates some ordering properties of the residual lives and the inactivity times of coherent systems with dependent exchangeable absolutely continuous components, based on the stochastically ordered signatures between systems, extending the results of Li and Zhang [2008. Some stochastic comparisons of conditional coherent systems. Applied Stochastic Models in Business and Industry 24, 541–549] for the case of ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 140, no. 2, pp. 454-460, 2010]]>In this paper we compare the hazard rate functions of two parallel systems, each of which consists of two independent components with exponential distribution functions. The paper gives various conditions under which there exists a hazard rate ordering between the two parallel systems. It is also shown that some of these conditions are both sufficient and necessary. In particular, it ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 140, no. 2, pp. 444-453, 2010]]>In this paper we investigate nonparametric estimation of some functionals of the conditional distribution of a scalar response variable Y given a random variable X taking values in a semi-metric space. These functionals include the regression function, the conditional cumulative distribution, the conditional density and some other ones. The literature on nonparametric functional statistics is only concerning pointwise consistency ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 140, no. 2, pp. 335-352, 2010]]>We derive expressions for the probability that an individual order statistic is closest to the target parameter among the order statistics from a complete random sample. Results are given for random variables with bounded and complete support. We then apply these general results to location-scale parameter families of distributions with specific applications to estimation of percentiles. In this case, ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 140, no. 9, pp. 2408-2415, 2010]]>The q-Bernstein basis, used in the definition of the q-Bernstein polynomials, is shown to be the probability mass function of a q-binomial distribution. This distribution is defined on a sequence of zero–one Bernoulli trials with probability of failure at any trial increasing geometrically with the number of previous failures. A modification of this model, with the ...

Journal: Journal of Statistical Planning and Inference - J STATIST PLAN INFER, vol. 140, no. 8, pp. 2184-2190, 2010]]>