Title

Determining the dimensionality in sliced inverse regression

Keywords

Eigenprojection; Elliptically symmetric distribution; General regression model; Projection matrix

Abstract

A general regression problem is one in which a response variable can be expressed as some function of one or more different linear combinations of a set of explanatory variables as well as a random error term. Sliced inverse regression is a method for determining these linear combinations. In this article we address the problem of determining how many linear combinations are involved. Procedures based on conditional means and conditional covariance matrices, as well as a procedure combining the two approaches, are considered. In each case we develop a test that has an asymptotic chi-squared distribution when the vector of explanatory variables is sampled from an elliptically symmetric distribution. © 1994 Taylor & Francis Group, LLC.

Publication Date

1-1-1994

Publication Title

Journal of the American Statistical Association

Volume

89

Issue

425

Number of Pages

141-148

Document Type

Article

Identifier

scopus

Personal Identifier

scopus

DOI Link

https://doi.org/10.1080/01621459.1994.10476455

Socpus ID

21344478847 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/21344478847

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