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An expectation–maximization algorithm for the matrix normal distribution with an application in remote sensing


  • Glanz, Hunter
  • Carvalho, Luis


Dramatic increases in the size and dimensionality of many modern datasets make crucial the need for sophisticated methods that can exploit inherent structure and handle missing values. In this article we derive an expectation–maximization (EM) algorithm for the matrix normal distribution, a distribution well-suited for naturally structured data such as spatio-temporal data. We review previously established maximum likelihood matrix normal estimates, and then consider the situation involving missing data. We apply our EM method in a simulation study exploring errors across different dimensions and proportions of missing data. We compare these errors to those from three alternative methods and show that our proposed EM method outperforms them in all scenarios. Finally, we implement the proposed EM method in a novel way on a satellite image dataset to investigate land-cover classification separability.

Suggested Citation

  • Glanz, Hunter & Carvalho, Luis, 2018. "An expectation–maximization algorithm for the matrix normal distribution with an application in remote sensing," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 31-48.
  • Handle: RePEc:eee:jmvana:v:167:y:2018:i:c:p:31-48
    DOI: 10.1016/j.jmva.2018.03.010

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    References listed on IDEAS

    1. Joseph G. Ibrahim & Ming-Hui Chen & Stuart R. Lipsitz & Amy H. Herring, 2005. "Missing-Data Methods for Generalized Linear Models: A Comparative Review," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 332-346, March.
    2. Roś, Beata & Bijma, Fetsje & de Munck, Jan C. & de Gunst, Mathisca C.M., 2016. "Existence and uniqueness of the maximum likelihood estimator for models with a Kronecker product covariance structure," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 345-361.
    3. Dayanand Naik & Shantha Rao, 2001. "Analysis of multivariate repeated measures data with a Kronecker product structured covariance matrix," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(1), pages 91-105.
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    Cited by:

    1. Kenneth Lange & Hua Zhou, 2022. "A Legacy of EM Algorithms," International Statistical Review, International Statistical Institute, vol. 90(S1), pages 52-66, December.

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