# Parameter Estimation For Multivariate Generalized Gaussian Distributions

1 SONDRA - Laboratoire franco-singapourien de recherche en électromagnétisme et radars 2 IMS - Laboratoire de l-intégration, du matériau au système 3 IRIT - Institut de recherche en informatique de Toulouse

Abstract : Due to its heavy-tailed and fully parametric form, the multivariate generalized Gaussian distribution MGGD has been receiving much attention in signal and image processing applications. Considering the estimation issue of the MGGD parameters, the main contribution of this paper is to prove that the maximum likelihood estimator MLE of the scatter matrix exists and is unique up to a scalar factor, for a given shape parameter $\beta\in0,1$. Moreover, an estimation algorithm based on a Newton-Raphson recursion is proposed for computing the MLE of MGGD parameters. Various experiments conducted on synthetic and real data are presented to illustrate the theoretical derivations in terms of number of iterations and number of samples for different values of the shape parameter. The main conclusion of this work is that the parameters of MGGDs can be estimated using the maximum likelihood principle with good performance.

Keywords : Multivariate generalized Gaussian distribution covariance matrix estimation fixed point algorithm

Author: Frédéric Pascal - Lionel Bombrun - Jean-Yves Tourneret - Yannick Berthoumieu -

Source: https://hal.archives-ouvertes.fr/