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March, 1989 On $M$-Processes and $M$-Estimation
A. H. Welsh
Ann. Statist. 17(1): 337-361 (March, 1989). DOI: 10.1214/aos/1176347021

Abstract

We relate the asymptotic behavior of $M$-estimators of the regression parameter in a linear model in which the dimension of the regression parameter may increase with the sample size to the stochastic equicontinuity of an associated $M$-process. The approach synthesises a number of results for the dimensionally fixed regression model and then extends these results in a direct unified way. The resulting theorems require only mild conditions on the $\psi$-function and the underlying distribution function. In particular, the results do not require $\psi$ to be smooth and hence can be applied to such estimators as the least absolute deviations estimator. We also treat one-step $M$-estimation.

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A. H. Welsh. "On $M$-Processes and $M$-Estimation." Ann. Statist. 17 (1) 337 - 361, March, 1989. https://doi.org/10.1214/aos/1176347021

Information

Published: March, 1989
First available in Project Euclid: 12 April 2007

zbMATH: 0701.62074
MathSciNet: MR981455
Digital Object Identifier: 10.1214/aos/1176347021

Subjects:
Primary: 62G05
Secondary: 60F05, 62J05

Rights: Copyright © 1989 Institute of Mathematical Statistics

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Vol.17 • No. 1 • March, 1989
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