Response dimension reduction for the conditional mean in multivariate regression

Jae Keun Yoo; R. Dennis Cook

doi:10.1016/j.csda.2008.07.029

Response dimension reduction for the conditional mean in multivariate regression

Jae Keun Yoo, R. Dennis Cook

Statistics (Twin Cities)

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

9 Scopus citations

Abstract

Sufficient dimension reduction methodologies in regression have been developed in the past decade, focusing mostly on predictors. Here, we propose a methodology to reduce the dimension of the response vector in multivariate regression, without loss of information about the conditional mean. The asymptotic distributions of dimension test statistics are chi-squared distributions, and an estimate of the dimension reduction subspace is asymptotically efficient. Moreover, the proposed methodology enables us to test response effects for the conditional mean. Properties of the proposed method are studied via simulation.

Original language	English (US)
Pages (from-to)	334-343
Number of pages	10
Journal	Computational Statistics and Data Analysis
Volume	53
Issue number	2
DOIs	https://doi.org/10.1016/j.csda.2008.07.029
State	Published - Dec 15 2008

Bibliographical note

Funding Information:
The authors are grateful to the referees for many helpful comments. The second author was supported in part by National Science Foundation Grant DMS-0405360.

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10.1016/j.csda.2008.07.029

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abstract = "Sufficient dimension reduction methodologies in regression have been developed in the past decade, focusing mostly on predictors. Here, we propose a methodology to reduce the dimension of the response vector in multivariate regression, without loss of information about the conditional mean. The asymptotic distributions of dimension test statistics are chi-squared distributions, and an estimate of the dimension reduction subspace is asymptotically efficient. Moreover, the proposed methodology enables us to test response effects for the conditional mean. Properties of the proposed method are studied via simulation.",

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AB - Sufficient dimension reduction methodologies in regression have been developed in the past decade, focusing mostly on predictors. Here, we propose a methodology to reduce the dimension of the response vector in multivariate regression, without loss of information about the conditional mean. The asymptotic distributions of dimension test statistics are chi-squared distributions, and an estimate of the dimension reduction subspace is asymptotically efficient. Moreover, the proposed methodology enables us to test response effects for the conditional mean. Properties of the proposed method are studied via simulation.

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Response dimension reduction for the conditional mean in multivariate regression

Abstract

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