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Biometrika Advance Access originally published online on April 15, 2008
Biometrika 2008 95(2):469-479; doi:10.1093/biomet/asn002
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© 2008 Biometrika Trust

Articles

Determining the dimension of the central subspace and central mean subspace

Peng Zeng

Department of Mathematics and Statistics, Auburn University, 221 Parker Hall, Auburn, Alabama 36849, U.S.A. zengpen{at}auburn.edu

Received for publication 1 June 2006. Revision received 1 December 2007.
  Abstract

The central subspace and central mean subspace are two important targets of sufficient dimension reduction. We propose a weighted chi-squared test to determine their dimensions based on matrices whose column spaces are exactly equal to the central subspace or the central mean subspace. The asymptotic distribution of the test statistic is obtained. Simulation examples are used to demonstrate the performance of this test.

Key Words: Central mean subspace • Central subspace • Sufficient dimension reduction • Weighted chi-squared test


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