Minimax hypothesis testing about the density support. (English) Zbl 0987.62030

Gayraud, Ghislaine

Bernoulli 7, No. 3, 507-525 (2001).

Summary: The 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 \({\mathcal G}\) of compact sets with smooth upper surface called boundary fragments. It is required to distinguish the simple null hypothesis specified by a known set \(G_0\) in \({\mathcal G}\) against the nonparametric alternative that \(G\) belongs to a class obtained by removing a certain neighbourhood of \(G_0\) in \({\mathcal G}\). Using the asymptotic minimax approach, the problem is to determine the order of the smallest distance between the null hypothesis \(H_0\) and the alternatives for which one is able to test the null hypothesis against the alternatives with a given summarized error.

MSC:

62G10	Nonparametric hypothesis testing
62C20	Minimax procedures in statistical decision theory

Keywords:

minimax rate of testing; underlying support