Testing local hypotheses with different types of incomplete data

Abstract

In this work, we consider a general framework of incomplete data which includes many types of censoring and truncation models. Under this framework and assuming that the distribution of interest has a parametric form, we propose local tests for simple and composite hypotheses on the parameter. These tests are based on the φ−divergences, Wald and Rao statistics. We study the asymptotic behaviour of these statistics under the null hypothesis. For the φ−divergences statistics, we study the asymptotic behaviour under the alternative as well. This allows us to approximate the power function of the proposed tests. We also propose local tests of homogeneity which serve to compare the distributions of two samples. Finally, we present the results of an application on real data.