Title

Sufficient Dimension Reduction Via Inverse Regression: A Minimum Discrepancy Approach

Keywords

Inverse regression estimator; Sliced average variance estimation; Sliced inverse regression; Sufficient dimension reduction

Abstract

A family of dimension-reduction methods, the inverse regression (IR) family, is developed by minimizing a quadratic objective function. An optimal member of this family, the inverse regression estimator (IRE), is proposed, along with inference methods and a computational algorithm. The IRE has at least three desirable properties: (1) Its estimated basis of the central dimension reduction subspace is asymptotically efficient, (2) its test statistic for dimension has an asymptotic chi-squared distribution, and (3) it provides a chi-squared test of the conditional independence hypothesis that the response is independent of a selected subset of predictors given the remaining predictors. Current methods like sliced inverse regression belong to a suboptimal class of the IR family. Comparisons of these methods are reported through simulation studies. The approach developed here also allows a relatively straightforward derivation of the asymptotic null distribution of the test statistic for dimension used in sliced average variance estimation. © 2005 American Statistical Association.

Publication Date

6-1-2005

Publication Title

Journal of the American Statistical Association

Volume

100

Issue

470

Number of Pages

410-428

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1198/016214504000001501

Socpus ID

20444454672 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/20444454672

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