On the likelihood ratio test for envelope models in multivariate linear regression

    Authors

    J. R. Schott

    Comments

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    Abbreviated Journal Title

    Biometrika

    Keywords

    Asymptotic null distribution; Envelope model; Likelihood ratio test; Multivariate linear regression; Partial envelope model; Saddlepoint; approximation; Biology; Mathematical & Computational Biology; Statistics & Probability

    Abstract

    We investigate the likelihood ratio test for a hypothesis regarding the dimension of the Sigma-envelope of span(beta) in a multivariate linear regression model. The asymptotic null distribution of the likelihood ratio statistic is obtained as some nuisance parameters approach infinity. A saddlepoint approximation is also given for this limiting distribution. The accuracy of this approximation and its comparison to the standard chi-squared approximation are assessed via simulation. The results can be used in a similar test for partial envelope models.

    Journal Title

    Biometrika

    Volume

    100

    Issue/Number

    2

    Publication Date

    1-1-2013

    Document Type

    Article

    Language

    English

    First Page

    531

    Last Page

    537

    WOS Identifier

    WOS:000319428000020

    ISSN

    0006-3444

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