Determining The Dimensionality In Sliced Inverse Regression

    Authors

    J. R. Schott

    Comments

    Authors: contact us about adding a copy of your work at STARS@ucf.edu

    Abbreviated Journal Title

    J. Am. Stat. Assoc.

    Keywords

    EIGENPROJECTION; ELLIPTICALLY SYMMETRICAL DISTRIBUTION; GENERAL; REGRESSION MODEL; PROJECTION MATRIX; REDUCTION; Statistics & Probability

    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.

    Journal Title

    Journal of the American Statistical Association

    Volume

    89

    Issue/Number

    425

    Publication Date

    1-1-1994

    Document Type

    Article

    Language

    English

    First Page

    141

    Last Page

    148

    WOS Identifier

    WOS:A1994MY54600016

    ISSN

    0162-1459

    Share

    COinS