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Asymptotic Equivalence
Linear Model
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Estimating Regression Coefficients by Minimizing the Dispersion of the Residuals
Estimating Regression Coefficients by Minimizing the Dispersion of the Residuals,10.1214/aoms/1177692377,The Annals of Mathematical Statistics,Louis A
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Estimating Regression Coefficients by Minimizing the Dispersion of the Residuals
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Citations: 161
)
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Louis A. Jaeckel
An appealing approach to the problem of estimating the regression coefficients in a
linear model
is to find those values of the coefficients which make the residuals as small as possible. We give some measures of the dispersion of a set of numbers, and define our estimates as those values of the parameters which minimize the dispersion of the residuals. We consider dispersion measures which are certain linear combinations of the ordered residuals. We show that the estimates derived from them are asymptotically equivalent to estimates recently proposed by Jureckova. In the case of a single parameter, we show that our estimate is a "weighted median" of the pairwise slopes $(Y_j  Y_i)/(c^j  c^i)$.
Journal:
The Annals of Mathematical Statistics
, vol. 43, no. 1972, pp. 14491458, 1972
DOI:
10.1214/aoms/1177692377
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Citation Context
(40)
...This method was proposed by Jaeckel (
1972
)...
Yankun Gong
,
et al.
On the Iteratively Reweighted Rank Regression Estimator
...For each center
j
, consider Jaeckel's (
1972
) dispersion function given by where ‖·‖
_{ j }
is the pseudonorm and
R
_{j}
(
v
_{i}
) denotes the rank of
v
_{i}
among
M. Mushfiqur Rashid
,
et al.
R Estimates and Associated Inferences for Mixed Models With Covariates...
...We are interested in asymptotic properties of the rank regression estimate of β
_{0}
defined by Jaeckel
1
...
Kristi Kuljus
,
et al.
Asymptotic properties of a rank estimate in linear regression with sym...
...The LAD step can be seen as a rankbased estimator via Wilcoxon scores, to minimize the residual dispersion function given in
Jaeckel (1972)
...
Chenlei Leng
.
VARIABLE SELECTION AND COEFFICIENT ESTIMATION VIA REGULARIZED RANK REG...
...Rankbased estimates of the regression coefficients of an univariate linear model have been proposed by Jaeckel
(1972)
and Jureckova
(1971)
, which achieved some robustness against outliers, while allowing the user a choice of scores for efficiency consideration...
Weihua Zhou
.
A multivariate Wilcoxon regression estimate
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Citations
(161)
On the Iteratively Reweighted Rank Regression Estimator
Yankun Gong
,
Asheber Abebe
Journal:
Communications in Statisticssimulation and Computation  COMMUN STATISTSIMULAT COMPUT
, vol. 41, no. 2, pp. 155166, 2012
R Estimates and Associated Inferences for Mixed Models with Covariates in a MultiCenter Clinical Trial
M. Mushfiqur Rashid
,
Joseph W. McKean
,
John D. Kloke
Published in 2012.
R Estimates and Associated Inferences for Mixed Models With Covariates in a Multicenter Clinical Trial
M. Mushfiqur Rashid
,
Joseph W. McKean
,
John D. Kloke
Published in 2012.
A DistributionFree, Robust Method for Monitoring Linear Profiles Using RankBased Regression
Xuemin Zi
,
Changliang Zou
,
Fugee Tsung
Journal:
Iie Transactions
, vol. justaccep, no. justaccep, 2012
A distributionfree robust method for monitoring linear profiles using rankbased regression
Xuemin Zi
,
Changliang Zou
,
Fugee Tsung
Journal:
Iie Transactions
, vol. 44, no. 11, pp. 949963, 2012