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March, 1973 Inadmissibility of Maximum Likelihood Estimators in Some Multiple Regression Problems with Three or More Independent Variables
A. J. Baranchik
Ann. Statist. 1(2): 312-321 (March, 1973). DOI: 10.1214/aos/1176342368

Abstract

Consider a multiple regression problem in which the dependent variable and (3 or more) independent variables have a joint normal distribution. This problem was investigated some time ago by Charles Stein, who proposed reasonable loss functions for various problems involving estimation of the regression coefficients and who obtained various minimax and admissibility results. In this paper we continue this investigation and establish the inadmissibility of the traditional maximum likelihood estimators. Inadmissibility is proved by exhibiting explicit procedures having lower risk than the corresponding maximum likelihood procedure. These results are given in Theorems 1 and 2 of Section 3.

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A. J. Baranchik. "Inadmissibility of Maximum Likelihood Estimators in Some Multiple Regression Problems with Three or More Independent Variables." Ann. Statist. 1 (2) 312 - 321, March, 1973. https://doi.org/10.1214/aos/1176342368

Information

Published: March, 1973
First available in Project Euclid: 12 April 2007

zbMATH: 0271.62010
MathSciNet: MR348928
Digital Object Identifier: 10.1214/aos/1176342368

Rights: Copyright © 1973 Institute of Mathematical Statistics

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Vol.1 • No. 2 • March, 1973
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