Variance estimation in high dimensional regression models

Research output: Contribution to journalArticle

8 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)497-515
Number of pages19
JournalStatistica Sinica
Volume10
Issue number2
StatePublished - Apr 1 2000

Fingerprint

Variance Estimation
Bootstrap
Regression Model
High-dimensional
Least Squares Estimate
Linear Regression Model
Sample Size
Estimator
Regression model
Variance estimation

Keywords

  • Bootstrap
  • Dimension asymptotics
  • Jackknife
  • Many parameter regression
  • Variance estimation

Cite this

Variance estimation in high dimensional regression models. / Chatterjee, Snigdhansu; Bose, Arup.

In: Statistica Sinica, Vol. 10, No. 2, 01.04.2000, p. 497-515.

Research output: Contribution to journalArticle

@article{81a202ace531464296d08586a275c439,
title = "Variance estimation in high dimensional regression models",
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).",
keywords = "Bootstrap, Dimension asymptotics, Jackknife, Many parameter regression, Variance estimation",
author = "Snigdhansu Chatterjee and Arup Bose",
year = "2000",
month = "4",
day = "1",
language = "English (US)",
volume = "10",
pages = "497--515",
journal = "Statistica Sinica",
issn = "1017-0405",
publisher = "Institute of Statistical Science",
number = "2",

}

TY - JOUR

T1 - Variance estimation in high dimensional regression models

AU - Chatterjee, Snigdhansu

AU - Bose, Arup

PY - 2000/4/1

Y1 - 2000/4/1

N2 - 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).

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).

KW - Bootstrap

KW - Dimension asymptotics

KW - Jackknife

KW - Many parameter regression

KW - Variance estimation

UR - http://www.scopus.com/inward/record.url?scp=0034377904&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034377904&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0034377904

VL - 10

SP - 497

EP - 515

JO - Statistica Sinica

JF - Statistica Sinica

SN - 1017-0405

IS - 2

ER -