Variance estimation in high dimensional regression models

Snigdhansu Chatterjee; Arup Bose

Variance estimation in high dimensional regression models

Snigdhansu Chatterjee, Arup Bose

Statistics (Twin Cities)

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9 Scopus citations

Abstract

We treat the problem of variance estimation of the least squares estimate of the parameter in high dimensional linear regression models by using the Uncorrelated Weights Bootstrap (UBS). We find a representation of the UBS dispersion matrix and show that the bootstrap estimator is consistent if p²/n → 0 where p is the dimension of the parameter and n is the sample size. For fixed dimension we show that the UBS belongs to the R-class as defined in Liu and Singh (1992).

Original language	English (US)
Pages (from-to)	497-515
Number of pages	19
Journal	Statistica Sinica
Volume	10
Issue number	2
State	Published - Apr 1 2000

Keywords

Bootstrap
Dimension asymptotics
Jackknife
Many parameter regression
Variance estimation

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AB - We treat the problem of variance estimation of the least squares estimate of the parameter in high dimensional linear regression models by using the Uncorrelated Weights Bootstrap (UBS). We find a representation of the UBS dispersion matrix and show that the bootstrap estimator is consistent if p2/n → 0 where p is the dimension of the parameter and n is the sample size. For fixed dimension we show that the UBS belongs to the R-class as defined in Liu and Singh (1992).

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KW - Dimension asymptotics

KW - Jackknife

KW - Many parameter regression

KW - Variance estimation

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Variance estimation in high dimensional regression models

Abstract

Keywords

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