Open Access
December, 1987 On Preliminary Test and Shrinkage $M$-Estimation in Linear Models
Pranab Kumar Sen, A. K. M. Ehsanes Saleh
Ann. Statist. 15(4): 1580-1592 (December, 1987). DOI: 10.1214/aos/1176350611

Abstract

In a general univariate linear model, $M$-estimation of a subset of parameters is considered when the complementary subset is plausibly redundant. Along with the classical versions, both the preliminary test and shrinkage versions of the usual $M$-estimators are considered and, in the light of their asymptotic distributional risks, the relative asymptotic risk-efficiency results are studied in detail. Though the shrinkage $M$-estimators may dominate their classical versions, they do not, in general, dominate the preliminary test versions.

Citation

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Pranab Kumar Sen. A. K. M. Ehsanes Saleh. "On Preliminary Test and Shrinkage $M$-Estimation in Linear Models." Ann. Statist. 15 (4) 1580 - 1592, December, 1987. https://doi.org/10.1214/aos/1176350611

Information

Published: December, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0639.62046
MathSciNet: MR913575
Digital Object Identifier: 10.1214/aos/1176350611

Subjects:
Primary: 62C16
Secondary: 62F10 , 62G05 , 62H12

Keywords: $M$-estimators , Asymptotic distributional risk , asymptotic distributional risk efficiency , James-Stein rule , linear model , local alternatives , minimaxity , preliminary test , robustness , shrinkage estimator

Rights: Copyright © 1987 Institute of Mathematical Statistics

Vol.15 • No. 4 • December, 1987
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