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March, 1989 Asymptotics with Increasing Dimension for Robust Regression with Applications to the Bootstrap
Enno Mammen
Ann. Statist. 17(1): 382-400 (March, 1989). DOI: 10.1214/aos/1176347023

Abstract

A stochastic expansion for $M$-estimates in linear models with many parameters is derived under the weak condition $\kappa n^{1/3}(\log n)^{2/3} \rightarrow 0$, where $n$ is the sample size and $\kappa$ the maximal diagonal element of the hat matrix. The expansion is used to study the asymptotic distribution of linear contrasts and the consistency of the bootstrap. In particular, it turns out that bootstrap works in cases where the usual asymptotic approach fails.

Citation

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Enno Mammen. "Asymptotics with Increasing Dimension for Robust Regression with Applications to the Bootstrap." Ann. Statist. 17 (1) 382 - 400, March, 1989. https://doi.org/10.1214/aos/1176347023

Information

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

zbMATH: 0674.62017
MathSciNet: MR981457
Digital Object Identifier: 10.1214/aos/1176347023

Subjects:
Primary: 62E20
Secondary: 62F35, 62J05

Rights: Copyright © 1989 Institute of Mathematical Statistics

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Vol.17 • No. 1 • March, 1989
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