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Biometrika 2003 90(2):411-421; doi:10.1093/biomet/90.2.411
© 2003 by Biometrika Trust
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Weighted chi-squared tests for partial common principal component subspaces

James R.Schott1

1 Department of Statistics, University of Central Florida, Orlando, Florida 32816-2370, U.S.Ajschott{at}pegasus.cc.ucf.edu

We consider tests of the null hypothesis that g covariance matrices have a partial common principal component subspace of dimension s.Our approach uses a dimensionality matrix which has its rank equal to s when the hypothesis holds. The test can then be based on a statistic computed from the eigenvalues of an estimate of this dimensionality matrix. The asymptotic distribution of this statistic is that of a linear combination of independent one-degree-of-freedom chi-squared random variables. Simulation results indicate that this test yields significance levels that come closer to the nominal level than do those of a previously proposed method. The procedure is also extended to a test that g correlation matrices have a partial common principal component subspace.

Key Words: Correlation matrix; Dimensionality reduction; Principal components analysis

Received May 2002. Revised August 2002


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