Multivariate elliptical models, which include the well-known multivariate normal one, have attracted considerable attention in the recent literature.

In this thesis, we mainly consider the problem of estimating the precision matrix and its trace from a decision-theoretic point of view. Especially, we investigate three multivariate elliptical models, namely Kotz, Pearson type II and Bessel models.

We propose new estimators, that are obtained under a quadratic loss and a squared loss functions. The conditions under which the proposed estimators dominate the usual ones are established. Explicit expressions for the risk functions of the proposed and the usual estimators are also derived.

On an other hand, a method of mixture is used and allow us to find some news subclasses of elliptical distributions.

A stochastic representation, which is a consequence of a theorem of Schoenberg, is exploited in order to settle a closed form for the characteristic function of the multivariate Bessel distributions.