Tests for Kronecker envelope models in multilinear principal components analysis

    Authors

    J. R. Schott

    Comments

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    Abbreviated Journal Title

    Biometrika

    Keywords

    Asymptotic null distribution; Likelihood ratio test; Saddlepoint; approximation; MATRIX; Biology; Mathematical & Computational Biology; Statistics & Probability

    Abstract

    We develop likelihood methods for the Kronecker envelope model in the principal components analysis of matrix observations that have a multivariate normal distribution. Maximum likelihood estimates are derived and the associated likelihood ratio statistic for a test of this Knonecker envelope model is obtained. The asymptotic null distribution of the likelihood ratio statistic is derived as some nuisance parameters approach infinity, and a saddlepoint approximation for this limiting distribution is given. An alternative composite test for the Kronecker envelope model, which can be used when the sample size is too small to use the likelihood ratio test, is also given. Simulation results demonstrate the accuracy of our approximations.

    Journal Title

    Biometrika

    Volume

    101

    Issue/Number

    4

    Publication Date

    1-1-2014

    Document Type

    Article

    Language

    English

    First Page

    978

    Last Page

    984

    WOS Identifier

    WOS:000345827900017

    ISSN

    0006-3444

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