Generalized variance estimators in the multivariate gamma models

Philippe Bernardoff (1) , Célestin Kokonendji (1) , Bénédicte Puig (1)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

It has been shown that the uniformly minimum variance unbiased (UMVU) estimator of the generalized variance always exists for any natural exponential family. In practice, however, this estimator is often difficult to obtain. This paper explicitly identifies the results in complete bivariate and symmetric multivariate gamma models, which are diagonal quadratic exponential families. For the non-independent multivariate gamma models, it is then pointed out that the UMVU and the maximum likelihood estimators are not proportional as conjectured for models belonging in certain quadratic exponential families.

Mots clés: Determinant; Diagonal variance function; Maximum likelihood estimator; Natural exponential family; UMVU estimator

Domaines: Probabilités [math.PR]; Statistiques [math.ST]

Philippe Bernardoff, Célestin Kokonendji, Bénédicte Puig. Generalized variance estimators in the multivariate gamma models. 2006. ⟨hal-00221138⟩