Dimension reduction for conditional mean in regression (original) (raw)

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April 2002 Dimension reduction for conditional mean in regression

R.Dennis Cook,Bing Li

Ann. Statist. 30(2): 455-474 (April 2002). DOI: 10.1214/aos/1021379861

Abstract

In many situations regression analysis is mostly concerned with inferring about the conditional mean of the response given the predictors, and less concerned with the other aspects of the conditional distribution. In this paper we develop dimension reduction methods that incorporate this consideration. We introduce the notion of the Central Mean Subspace (CMS), a natural inferential object for dimension reduction when the mean function is of interest. We study properties of the CMS, and develop methods to estimate it. These methods include a new class of estimators which requires fewer conditions than pHd, and which displays a clear advantage when one of the conditions for pHd is violated. CMS also reveals a transparent distinction among the existing methods for dimension reduction: OLS, pHd, SIR and SAVE. We apply the new methods to a data set involving recumbent cows.

Citation

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R.Dennis Cook. Bing Li. "Dimension reduction for conditional mean in regression." Ann. Statist. 30 (2) 455 - 474, April 2002. https://doi.org/10.1214/aos/1021379861

Information

Published: April 2002

First available in Project Euclid: 14 May 2002

Digital Object Identifier: 10.1214/aos/1021379861

Subjects:

Primary: 62G08

Secondary: 62-09, 62H05

Keywords: central subspace, graphics, pHd, regression, SAVE, SIR, visualization