The Annals of Statistics

Asymptotics with Increasing Dimension for Robust Regression with Applications to the Bootstrap

Enno Mammen

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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.

Article information

Source
Ann. Statist., Volume 17, Number 1 (1989), 382-400.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347023

Digital Object Identifier
doi:10.1214/aos/1176347023

Mathematical Reviews number (MathSciNet)
MR981457

Zentralblatt MATH identifier
0674.62017

JSTOR
links.jstor.org

Subjects
Primary: 62E20: Asymptotic distribution theory
Secondary: 62J05: Linear regression 62F35: Robustness and adaptive procedures

Keywords
$M$-estimators linear model bootstrap asymptotic normality dimension asymptotics

Citation

Mammen, Enno. Asymptotics with Increasing Dimension for Robust Regression with Applications to the Bootstrap. Ann. Statist. 17 (1989), no. 1, 382--400. doi:10.1214/aos/1176347023. https://projecteuclid.org/euclid.aos/1176347023


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