Strydom, NinaCrowther, N.A.S. (Nicolaas Andries Sadie), 1944-2017-10-252018Nina Strydom & Nico Crowther (2018) Multivariate normal estimation: the case (n < p), Communications in Statistics - Theory and Methods, 47:5, 1071-1090, DOI: 10.1080/03610926.2017.1316405.0361-0926 (print)1532-415X (online)10.1080/03610926.2017.1316405http://hdl.handle.net/2263/62917Estimation 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.en© 2017 Taylor & Francis Group, LLC. This is an electronic version of an article published in Communications in Statistics Theory and Methods , vol. 47, no. 5, pp. 1071-1090, 2018. doi : 10.1080/03610926.2017.1316405. Communications in Statistics Theory and Methods is available online at : http://www.tandfonline.comloi/lsta20.Linear growth in covariance matricesMaximum likelihood estimation under constraintsObservations less than parametersProportional covariance matricesProportional growth in covariance matricesSeemingly unrelated regressionCovariance matrixMatrix algebraMaximum likelihoodMultivariate observationsMultivariate normalFeasible solutionEstimabilityCovariance matricesPostprint Article