ASYMPTOTIC DISTRIBUTION OF ESTIMATED AFFINITY BETWEEN MULTIPARAMETER EXPONENTIAL FAMILIES*

STEVEN T. GARREN

Department of Statistics, University of Virginia, 104 Halsey Hall, Charlottesville, VA 22903, U.S.A.

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

Abstract. Let F_{1}, …, F_{J} be the distributions of J independent multiparameter exponential families, and ρ_{J}(F_{1}, …, F_{J}) denote the affinity between F_{1}, …, F_{J}. We consider the problem of estimating ρ_{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 ρ_{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.