A note on the maximum likelihood estimators for the location and scatter parameters of a multivariate Cauchy distribution


Arslan O., Kent J.

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, vol.27, no.12, pp.3007-3014, 1998 (SCI-Expanded) identifier identifier

Abstract

The likelihood function of a multivariate Cauchy distribution with unknown location and scatter parameters in p dimensions has a unique maximum provided the sample is in general position and is of size n > p + 1 (see Kent and Tyler 1991 and Kent et al., 1994). fn this paper, we show that when n = p + 1, the maximum of the location-scatter Cauchy likelihood function occurs when the parameters lie on a p-dimensional surface.