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Journal of the American Statistical Association Volume 104, 2009 - Issue 488
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Theory and Methods

Maximum Likelihood Estimation of the Multivariate Normal Mixture Model

Otilia Boldea Otilia Boldea is Assistant Professor and Jan R. Magnus is Professor of Econometrics , both at the Department of Econometrics & OR, Tilburg University, PO Box 90153, 5000 LE Tilburg, The Netherlands. The authors are grateful to Hamparsum Bozdogan for asking a question which led to this paper, to John Einmahl and Evangelos Evangelou for useful comments, to Geoffrey McLachlan for providing his EMMIX FORTRAN code free of charge and for his prompt response to our questions, and to the editor, associate editor, and the referees for helpful comments. The first version of this paper was written during a visit of one of us to the Wang Yanan Institute for Studies in Economics (WISE), Xiamen University, China.
&
Jan R. Magnus Otilia Boldea is Assistant Professor and Jan R. Magnus is Professor of Econometrics , both at the Department of Econometrics & OR, Tilburg University, PO Box 90153, 5000 LE Tilburg, The Netherlands. The authors are grateful to Hamparsum Bozdogan for asking a question which led to this paper, to John Einmahl and Evangelos Evangelou for useful comments, to Geoffrey McLachlan for providing his EMMIX FORTRAN code free of charge and for his prompt response to our questions, and to the editor, associate editor, and the referees for helpful comments. The first version of this paper was written during a visit of one of us to the Wang Yanan Institute for Studies in Economics (WISE), Xiamen University, China.
Pages 1539-1549 | Received 01 May 2008, Published online: 01 Jan 2012
 
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Abstract

The Hessian of the multivariate normal mixture model is derived, and estimators of the information matrix are obtained, thus enabling consistent estimation of all parameters and their precisions. The usefulness of the new theory is illustrated with two examples and some simulation experiments. The newly proposed estimators appear to be superior to the existing ones.

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