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(5)
Maximum Likelihood Estimate
Normal Distribution
Posterior Distribution
Random Variable
Regularity Condition
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Maximum Likelihood Estimation of a Translation Parameter of a Truncated Distribution
Maximum Likelihood Estimation of a Translation Parameter of a Truncated Distribution,10.1214/aoms/1177692707,The Annals of Mathematical Statistics,Mic
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Maximum Likelihood Estimation of a Translation Parameter of a Truncated Distribution
(
Citations: 8
)
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Michael Woodroofe
Let $f_\theta(x) = f(x  \theta), \theta, x\in R$, where $f(x) = 0$ for $x \leqq 0$ and let $\hat{\theta}_n$ be the
maximum likelihood estimate
(MLE) of $\theta$ based on a sample of size $n$. If $\alpha = \lim f'(x)$ exists as $x \rightarrow 0$, and $0 < \alpha < \infty$, then under some regularity conditions, it is shown that $\alpha_n(\hat{\theta}_n  \theta)$ has an asymptotic standard
normal distribution
where $2\alpha_n^2 = \alpha n \log n$ and that if $\theta$ is regarded as a
random variable
with a prior density, then the
posterior distribution
of $\alpha_n(\theta  \hat{\theta}_n)$ converges to normality in probability.
Journal:
The Annals of Mathematical Statistics
, vol. 43, no. 1972, pp. 113122, 1972
DOI:
10.1214/aoms/1177692707
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Citation Context
(2)
...For α = 2 and 1 < α <2 its rate is (
n
log
n
)
^{−1/2}
and
n
^{−1/α}
, respectively; see Woodroofe (
1972
,
1974
), and Akahira (
1975a
); for location models with additional parameters see Smith (
1985
)...
Ursula U. Müller
,
et al.
Estimation in Nonparametric Regression with NonRegular Errors
...(n3`logn) 1/2 (0 n  O) ~ n(O, 1), which generalises Woodroofe [
20
]...
R. L. Smith
,
et al.
Statistics of the threeparameter weibull distribution
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Citations
(8)
Estimation in Nonparametric Regression with NonRegular Errors
(
Citations: 1
)
Ursula U. Müller
,
Wolfgang Wefelmeyer
Journal:
Communications in Statisticstheory and Methods  COMMUN STATISTTHEOR METHOD
, vol. 39, no. 89, pp. 16191629, 2010
Indirect inference in structural econometric models
(
Citations: 1
)
Tong Li
Journal:
Journal of Econometrics  J ECONOMETRICS
, vol. 157, no. 1, pp. 120128, 2010
Bayesian likelihood methods for estimating the end point of a distribution
(
Citations: 1
)
Peter Hall
,
Julian Z. Wang
Journal:
Journal of The Royal Statistical Society Series Bstatistical Methodology  J ROY STAT SOC SER BSTAT MET
, vol. 67, no. 5, pp. 717729, 2005
Estimation of the Maximum Earthquake Magnitude, m max
(
Citations: 30
)
Andrzej Kijko
Journal:
Pure and Applied Geophysics  PURE APPL GEOPHYS
, vol. 161, no. 8, pp. 16551681, 2004
Rates of convergence of L p estimators for a density with an infinity cusp
Miguel A. Arcones
Journal:
Journal of Statistical Planning and Inference  J STATIST PLAN INFER
, vol. 81, no. 1, pp. 3350, 1999