f -DISSIMILARITY OF SEVERAL DISTRIBUTIONS IN TESTING STATISTICAL HYPOTHESES

K. ZOGRAFOS

Department of Mathematics, Probability-Statistics & Operational Research Unit, University of Ioannina, 45110 Ioannina, Greece

(Received July 15, 1996; revised June 30, 1997)

Abstract. Various problems in statistics have been treated by the decision rule, based on the concept of distance between distributions. The aim of this paper is to give an approach for testing statistical hypotheses, using a general class of dissimilarity measures among k ≥ 2 distributions. The test statistics are obtained by the replacement, in the expression of the dissimilarity measure, of the unknown parameters by their maximum likelihood estimators. The asymptotic distributions of the resulting test statistics are investigated and the results are applied to multinomial and multivariate normal populations.

Key words and phrases: f-dissimilarity, f-dissimilarity statistic, asymptotic distribution, multinomial distribution, multivariate normal distribution, testing statistical hypotheses.