Statistics and Probability; Statistics, Probability and Uncertainty
Abstract :
[en] A classical characterization result, which can be traced back to Gauss, states that the maximum likelihood estimator (MLE) of the location parameter equals the sample mean for any possible univariate samples of any possible sizes n if and only if the samples are drawn from a Gaussian population. A similar result, in the two-dimensional case, is given in von Mises (1918) for the Fisher-von Mises-Langevin (FVML) distribution, the equivalent of the Gaussian law on the unit circle. Half a century later, Bingham and Mardia (1975) extend the result to FVML distributions on the unit sphere (Formula Presented.), k ≥ 2. In this paper, we present a general MLE characterization theorem for a large subclass of rotationally symmetric distributions on SK-1, k ≥ 2, including the FVML distribution.
Disciplines :
Mathematics
Author, co-author :
Duerinckx, Mitia; Département de Mathématique, Université Libre de Bruxelles, Bruxelles, Belgium
LEY, Christophe ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) ; E.C.A.R.E.S. and Département de Mathématique, Université Libre de Bruxelles, Bruxelles, Belgium
External co-authors :
yes
Language :
English
Title :
Maximum likelihood characterization of rotationally symmetric distributions on the sphere
Acknowledgement. Christophe Ley thanks the Fonds National de la Recherche Scientifique, Communauté fran¸caise de Belgique, for support via a Mandat de Chargéde Recherche.
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