Estimation des matrices de précision et de covariance de modèles elliptiques multivariés

Diplôme Thèse Estimation des matrices de précision et de covariance de modèles elliptiques multivariés eng Estimation of the Precision Matrix and the Covariance Matrix of Multivariate Elliptical Models 2006-04-07 author Sarr Amadou 510417 director Streit Franz 25352 Administration de la faculté des sciences (SIAD) 116 10.13097/archive-ouverte/unige:187191 urn:nbn:ch:unige-1871919 Sc. 3731 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. Dewey 510 25 Section de mathématiques 11 false f94bf958-1952-4393-95c5-4e1f8227ee98 Thesis Public sarr_thèse.pdf 4407770 application/pdf Restricted 2106-04-07 083132637e924f881fb8316644f92bbacc5917e744218ead152f7f0ab378fd7e 196f1a6b-6300-4622-bc0c-3ea48bad615a Imprimatur Public sarr_imprimatur.pdf 18594 application/pdf c297eebbff2557c38635c308563bd6905c60a3a91c585f9256dec676d4695d75 embargoedAccess Faculté des sciences / Section de mathématiques

Title	Published in	Access level	OA Policy	Year	Views	Downloads

Estimation des matrices de précision et de covariance de modèles elliptiques multivariés				2006	124	1

Archive ouverte UNIGE

Sarr, Amadou