Multivariate normal estimation: the case (n

Nina Strydom and Nico Crowther

Communications in Statistics - Theory and Methods, 2018, vol. 47, issue 5, 1071-1090

Abstract: Estimation in the multivariate context when the number of observations available is less than the number of variables is a classical theoretical problem. In order to ensure estimability, one has to assume certain constraints on the parameters. A method for maximum likelihood estimation under constraints is proposed to solve this problem. Even in the extreme case where only a single multivariate observation is available, this may provide a feasible solution. It simultaneously provides a simple, straightforward methodology to allow for specific structures within and between covariance matrices of several populations. This methodology yields exact maximum likelihood estimates.

Date: 2018
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DOI: 10.1080/03610926.2017.1316405

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