Resumen de On UMVU estimator of the generalized variance for natural exponential families

Célestin C. Kokonendji

• For any given natural exponential family (NEF), the existence is proven for the uniformly minimum variance and unbiased (UMVU) estimator of the generalized variance, i.e. the determinant of the covariance matrix. This result provides a unification and a general extension of those appearing in recent literature. In order to compare the UMVU estimator with an unbiased maximum likelihood (ML) estimator, the necessary and sufficient condition will be given. Finally, a characterization of the Poisson-Gaussian laws in Rd will be given.