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Mathematical Methods of Statistics

, Volume 17, Issue 1, pp 66–73 | Cite as

Generalized variance estimators in the multivariate gamma models

  • Ph. BernardoffEmail author
  • C. Kokonendji
  • B. Puig
Article

Abstract

It is already known that the uniformly minimum variance unbiased (UMVU) estimator of the generalized variance always exists for any natural exponential family. However, in practice, this estimator is often difficult to obtain. This paper provides explicit forms of the UMVU estimators for the bivariate and symmetric multivariate gamma models, which are diagonal quadratic exponential families. For the non-independent multivariate gamma models, it is shown that the UMVU and the maximum likelihood estimators are not proportional.

Key words

diagonal variance function maximum likelihood estimator natural exponential family UMVU estimator 

2000 Mathematics Subject Classification

62F10 62H12 62H99 

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Copyright information

© Allerton Press Inc. 2008

Authors and Affiliations

  1. 1.Laboratoire de mathématiques appliquées, UMR 5142 CNRSUniversité de Pau et des Pays de l’AdourPauFrance

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