The Annals of Statistics

On Preliminary Test and Shrinkage $M$-Estimation in Linear Models

Pranab Kumar Sen and A. K. M. Ehsanes Saleh

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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.

Article information

Source
Ann. Statist., Volume 15, Number 4 (1987), 1580-1592.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176350611

Digital Object Identifier
doi:10.1214/aos/1176350611

Mathematical Reviews number (MathSciNet)
MR913575

Zentralblatt MATH identifier
0639.62046

JSTOR
links.jstor.org

Subjects
Primary: 62C16
Secondary: 62G05: Estimation 62F10: Point estimation 62H12: Estimation

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

Citation

Sen, Pranab Kumar; Saleh, A. K. M. Ehsanes. On Preliminary Test and Shrinkage $M$-Estimation in Linear Models. Ann. Statist. 15 (1987), no. 4, 1580--1592. doi:10.1214/aos/1176350611. https://projecteuclid.org/euclid.aos/1176350611


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