Minimax hypothesis testing about the density support

Abstract

This paper is concerned with testing nonparametric hypotheses about the underlying support G of independent and identically distributed observations. It is assumed that G belongs to a class {\cal G} of compact sets with smooth upper surface called boundary fragments. It is required to distinguish the simple null hypothesis specified by a known set G₀ in {\cal G} against nonparametric alternatives that G belongs to a class obtained by removing a certain neighbourhood of G₀ in {\cal G}. Using the asymptotical minimax approach, the problem is to determine the order of the smallest distance between the null hypothesis H₀ and the alternatives for which one is able to test the null hypothesis against the alternatives with a given summarized error.