On testing local hypotheses via local divergence

The aim of this paper is to propose procedures that test statistical hypotheses locally, that is, assess the validity of a model in a specific domain of the data. In this context, the one and two sample problems will be discussed. The proposed tests are based on local divergences which are defined in such a way as to quantify the divergence between probability distributions locally, in a specific area of the joint domain of the underlined models. The theoretical results are exemplified using simulations and two real datasets.