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A likelihood ratio test for separability of covariances

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  • Mitchell, Matthew W.
  • Genton, Marc G.
  • Gumpertz, Marcia L.
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    Abstract

    We propose a formal test of separability of covariance models based on a likelihood ratio statistic. The test is developed in the context of multivariate repeated measures (for example, several variables measured at multiple times on many subjects), but can also apply to a replicated spatio-temporal process and to problems in meteorology, where horizontal and vertical covariances are often assumed to be separable. Separable models are a common way to model spatio-temporal covariances because of the computational benefits resulting from the joint space-time covariance being factored into the product of a covariance function that depends only on space and a covariance function that depends only on time. We show that when the null hypothesis of separability holds, the distribution of the test statistic does not depend on the type of separable model. Thus, it is possible to develop reference distributions of the test statistic under the null hypothesis. These distributions are used to evaluate the power of the test for certain nonseparable models. The test does not require second-order stationarity, isotropy, or specification of a covariance model. We apply the test to a multivariate repeated measures problem.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 97 (2006)
    Issue (Month): 5 (May)
    Pages: 1025-1043

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    Handle: RePEc:eee:jmvana:v:97:y:2006:i:5:p:1025-1043

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    Related research

    Keywords: Kronecker product Multivariate regression Multivariate repeated measures Nonstationary Separable covariance Spatio-temporal process;

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    Cited by:
    1. Fernández-Avilés, G & Montero, JM & Mateu, J, 2011. "Mathematical Genesis of the Spatio-Temporal Covariance Functions," MPRA Paper 35874, University Library of Munich, Germany.
    2. Manceur, A.M. & Dutilleul, P., 2013. "Unbiased modified likelihood ratio tests for simple and double separability of a variance–covariance structure," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 631-636.
    3. Wang, Lili & Paul, Debashis, 2014. "Limiting spectral distribution of renormalized separable sample covariance matrices when p/n→0," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 25-52.

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