AISM 52, 426-437

Asymptotic distribution of estimated affinity
between multiparameter exponential families

Steven T. Garren

(Received September 1, 1998; revised February 8, 1999)

Abstract.    Let F₁,..., F_J be the distributions of J independent multiparameter exponential families, and rho_J(F₁,..., F_J) denote the affinity between F₁,..., F_J. We consider the problem of estimating rho_J on the basis of independent random samples from these distributions. Subject to some mild regularity conditions, we derive the asymptotic distribution of the maximum likelihood estimator of rho_J. Applications to hypothesis testing and discriminant analysis are discussed, and an example is provided.

Key words and phrases:    Affinity, asymptotic distribution, distance measure, exponential family.

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