Marginal tests with sliced average variance estimation

Shao Yongwu; R. Dennis Cook; Sanford Weisberg

doi:10.1093/biomet/asm021

Marginal tests with sliced average variance estimation

Shao Yongwu
, R. Dennis Cook
, Sanford Weisberg

Statistics (Twin Cities)

Research output: Contribution to journal › Article › peer-review

48 Scopus citations

Abstract

We present a new computationally feasible test for the dimension of the central subspace in a regression problem based on sliced average variance estimation. We also provide a marginal coordinate test. Under the null hypothesis, both the test of dimension and the marginal coordinate test involve test statistics that asymptotically have chi-squared distributions given normally distributed predictors, and have a distribution that is a linear combination of chi-squared distributions in general.

Original language	English (US)
Pages (from-to)	285-296
Number of pages	12
Journal	Biometrika
Volume	94
Issue number	2
DOIs	https://doi.org/10.1093/biomet/asm021
State	Published - 2007

Bibliographical note

Funding Information:
ACKNOWLEDGEMENT We thank the referees and the editor for their useful comments. R. D. Cook and Y. Shao were supported by the U.S. National Science Foundation.

Keywords

Marginal coordinate test
Sufficient dimension reduction

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10.1093/biomet/asm021

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abstract = "We present a new computationally feasible test for the dimension of the central subspace in a regression problem based on sliced average variance estimation. We also provide a marginal coordinate test. Under the null hypothesis, both the test of dimension and the marginal coordinate test involve test statistics that asymptotically have chi-squared distributions given normally distributed predictors, and have a distribution that is a linear combination of chi-squared distributions in general.",

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AU - Dennis Cook, R.

AU - Weisberg, Sanford

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PY - 2007

Y1 - 2007

N2 - We present a new computationally feasible test for the dimension of the central subspace in a regression problem based on sliced average variance estimation. We also provide a marginal coordinate test. Under the null hypothesis, both the test of dimension and the marginal coordinate test involve test statistics that asymptotically have chi-squared distributions given normally distributed predictors, and have a distribution that is a linear combination of chi-squared distributions in general.

AB - We present a new computationally feasible test for the dimension of the central subspace in a regression problem based on sliced average variance estimation. We also provide a marginal coordinate test. Under the null hypothesis, both the test of dimension and the marginal coordinate test involve test statistics that asymptotically have chi-squared distributions given normally distributed predictors, and have a distribution that is a linear combination of chi-squared distributions in general.

KW - Marginal coordinate test

KW - Sufficient dimension reduction

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UR - https://www.scopus.com/pages/publications/34548461701#tab=citedBy

U2 - 10.1093/biomet/asm021

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JO - Biometrika

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ER -

Marginal tests with sliced average variance estimation

Abstract

Bibliographical note

Keywords

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