Abstract
In this paper we compare the uniformly minimum variance unbiased (UMVU) estimator and maximum likelihood (ML) estimator of the generalized variance in the context of natural exponential families (NEFs) on , d>1. We conjecture that for irreducible NEFs the proportionality holds if and only if the generalized variance has a specific form. In particular, we show that the estimators are proportional in the simple and homogeneous quadratic NEFs and prove that the UMVU estimator is preferable in terms of mean squared error except for the case of multinomial family.
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