THE MINIMUM PHI-DIVERGENCE ESTIMATES WITH FUZZY OBSERVATIONS - STATISTICAL APPLICATIONS

In this paper we consider statistical problems involving experiments w hose observation does not provide exact information, but that it may b e assimilated with fuzzy information. First, we present the minimum ph i-divergence estimator <(theta)over cap>(phi) for the unknown paramete r theta on the basis of the phi-divergence between the fuzzy statistic and the probability vector of the fuzzy information system based on a fuzzy random sample. Properties of this estimator are also used to ob tain the asymptotic distribution of the statistic associated to the mi nimum phi-divergence estimator. This asymptotic distribution is used t o give a testing procedure. (C) 1998 Elsevier Science B.V. All rights reserved.