Generalized variance estimators in the multivariate gamma models
نویسندگان
چکیده
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 di¢ cult to obtain. This paper explicitly identi es 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. AMS 2000 subject classi cation: 62F10; 62H12; 62H99
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