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Biometrika Advance Access published online on February 28, 2007
Biometrika, doi:10.1093/biomet/asm021
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Copyright © 2007 Biometrika Trust

Marginal tests with sliced average variance estimation

Yongwu Shao, R. Dennis Cook and Sanford Weisberg

School of Statistics, University of Minnesota, Minneapolis, Minnesota 55455, U.S.A.

ywshao{at}stat.umn.edu

dennis{at}stat.umn.edu

sandy{at}stat.umn.edu

Received for publication 1 December 2005. Revision received 1 June 2006.
  Abstract

We present a new computationally feasible test for the dimension of the central subspace in a regression problem based on sliced average variance estimation. We also provide a marginal coordinate test. Under the null hypothesis, both the test of dimension and the marginal coordinate test involve test statistics that asymptotically have chi-squared distributions given normally distributed predictors, and have a distribution that is a linear combination of chi-squared distributions in general.

Key Words: marginal coordinate test • sufficient dimension reduction


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