Weighted chi-squared tests for partial common principal component subspaces

    Authors

    J. R. Schott

    Abbreviated Journal Title

    Biometrika

    Keywords

    correlation matrix; dimensionality reduction; principal components; analysis; SAMPLE CORRELATION MATRIX; Biology; Mathematical & Computational Biology; Statistics & Probability

    Abstract

    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.

    Journal Title

    Biometrika

    Volume

    90

    Issue/Number

    2

    Publication Date

    1-1-2003

    Document Type

    Article

    Language

    English

    First Page

    411

    Last Page

    421

    WOS Identifier

    WOS:000183818500012

    ISSN

    0006-3444

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