Weighted envelope estimation to handle variability in model selection

D. J. Eck, R. D Cook

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Envelope methodology can provide substantial efficiency gains in multivariate statistical problems, but in some applications the estimation of the envelope dimension can induce selection volatility that may mitigate those gains. Current envelope methodology does not account for the added variance that can result from this selection. In this article, we circumvent dimension selection volatility through the development of a weighted envelope estimator. Theoretical justification is given for our estimator, and the validity of the residual bootstrap for estimating its asymptotic variance is established. A simulation study and real-data analysis illustrate the utility of our weighted envelope estimator.

Original languageEnglish (US)
Pages (from-to)743-749
Number of pages7
JournalBiometrika
Volume104
Issue number3
DOIs
StatePublished - Sep 1 2017

Fingerprint

Volatilization
Model Selection
Envelope
data analysis
Estimator
Volatility
methodology
Methodology
Asymptotic Variance
Justification
Bootstrap
Data analysis
Model selection
Simulation Study

Keywords

  • Dimension reduction
  • Envelope model
  • Model selection
  • Residual bootstrap
  • Variance reduction

Cite this

Weighted envelope estimation to handle variability in model selection. / Eck, D. J.; Cook, R. D.

In: Biometrika, Vol. 104, No. 3, 01.09.2017, p. 743-749.

Research output: Contribution to journalArticle

@article{9fb8b782ec414125b10b1cbf3590809c,
title = "Weighted envelope estimation to handle variability in model selection",
abstract = "Envelope methodology can provide substantial efficiency gains in multivariate statistical problems, but in some applications the estimation of the envelope dimension can induce selection volatility that may mitigate those gains. Current envelope methodology does not account for the added variance that can result from this selection. In this article, we circumvent dimension selection volatility through the development of a weighted envelope estimator. Theoretical justification is given for our estimator, and the validity of the residual bootstrap for estimating its asymptotic variance is established. A simulation study and real-data analysis illustrate the utility of our weighted envelope estimator.",
keywords = "Dimension reduction, Envelope model, Model selection, Residual bootstrap, Variance reduction",
author = "Eck, {D. J.} and Cook, {R. D}",
year = "2017",
month = "9",
day = "1",
doi = "10.1093/biomet/asx035",
language = "English (US)",
volume = "104",
pages = "743--749",
journal = "Biometrika",
issn = "0006-3444",
publisher = "Oxford University Press",
number = "3",

}

TY - JOUR

T1 - Weighted envelope estimation to handle variability in model selection

AU - Eck, D. J.

AU - Cook, R. D

PY - 2017/9/1

Y1 - 2017/9/1

N2 - Envelope methodology can provide substantial efficiency gains in multivariate statistical problems, but in some applications the estimation of the envelope dimension can induce selection volatility that may mitigate those gains. Current envelope methodology does not account for the added variance that can result from this selection. In this article, we circumvent dimension selection volatility through the development of a weighted envelope estimator. Theoretical justification is given for our estimator, and the validity of the residual bootstrap for estimating its asymptotic variance is established. A simulation study and real-data analysis illustrate the utility of our weighted envelope estimator.

AB - Envelope methodology can provide substantial efficiency gains in multivariate statistical problems, but in some applications the estimation of the envelope dimension can induce selection volatility that may mitigate those gains. Current envelope methodology does not account for the added variance that can result from this selection. In this article, we circumvent dimension selection volatility through the development of a weighted envelope estimator. Theoretical justification is given for our estimator, and the validity of the residual bootstrap for estimating its asymptotic variance is established. A simulation study and real-data analysis illustrate the utility of our weighted envelope estimator.

KW - Dimension reduction

KW - Envelope model

KW - Model selection

KW - Residual bootstrap

KW - Variance reduction

UR - http://www.scopus.com/inward/record.url?scp=85037093164&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85037093164&partnerID=8YFLogxK

U2 - 10.1093/biomet/asx035

DO - 10.1093/biomet/asx035

M3 - Article

AN - SCOPUS:85037093164

VL - 104

SP - 743

EP - 749

JO - Biometrika

JF - Biometrika

SN - 0006-3444

IS - 3

ER -