Goodness of fit tests with weights in the classes based on (h,phi)-divergences

Abstract

The aim of the paper is to present a test of goodness of fit with weigths in the classes based on weighted (h, phi)-divergences. This family of divergences generalizes in some sense the previous weighted divergences studied by Frank et al [5] and Kapur [11]. The weighted (h, phi)-divergence between an empirical distribution and a fixed distribution is here investigated for large simple random samples, and the asymptotic distributions are shown to be either normal or equal to the distribution of a linear combination of independent chi-square variables. Some approximations to the linear combination of independent chi-square variables are presented