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 language | English (US) |
|---|---|
| Pages (from-to) | 743-749 |
| Number of pages | 7 |
| Journal | Biometrika |
| Volume | 104 |
| Issue number | 3 |
| DOIs | |
| State | Published - Sep 1 2017 |
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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 journal › Article
}
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 -