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A likelihood ratio test for separability of covariances


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


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.

Suggested Citation

  • Mitchell, Matthew W. & Genton, Marc G. & Gumpertz, Marcia L., 2006. "A likelihood ratio test for separability of covariances," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1025-1043, May.
  • Handle: RePEc:eee:jmvana:v:97:y:2006:i:5:p:1025-1043

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    References listed on IDEAS

    1. Patrick E. Brown & Peter J. Diggle & Martin E. Lord & Peter C. Young, 2001. "Space-time calibration of radar rainfall data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 50(2), pages 221-241.
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    Cited by:

    1. Yuan Wang & Brian P. Hobbs & Jianhua Hu & Chaan S. Ng & Kim-Anh Do, 2015. "Predictive classification of correlated targets with application to detection of metastatic cancer using functional CT imaging," Biometrics, The International Biometric Society, vol. 71(3), pages 792-802, September.
    2. Samantha Leorato & Maura Mezzetti, 2015. "Spatial Panel Data Model with error dependence: a Bayesian Separable Covariance Approach," CEIS Research Paper 338, Tor Vergata University, CEIS, revised 09 Apr 2015.
    3. Filipiak, Katarzyna & Klein, Daniel & Roy, Anuradha, 2016. "Score test for a separable covariance structure with the first component as compound symmetric correlation matrix," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 105-124.
    4. 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.
    5. repec:eee:jmvana:v:158:y:2017:i:c:p:73-86 is not listed on IDEAS
    6. Fernández-Avilés, G & Montero, JM & Mateu, J, 2011. "Mathematical Genesis of the Spatio-Temporal Covariance Functions," MPRA Paper 35874, University Library of Munich, Germany.
    7. 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.
    8. Yin, Jianxin & Li, Hongzhe, 2012. "Model selection and estimation in the matrix normal graphical model," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 119-140.
    9. Viroli, Cinzia, 2012. "On matrix-variate regression analysis," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 296-309.


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