Estimation of Support of a Density

Abstract

Let X₁,…,X_n be i.i.d. random variables uniformly distributed in a closed set G ⊂ K=[0_/1]^N , mes G ≠ 0. In this chapter we study the problem of estimation of G, given the observations X₁,…,X_n . This problem is closely related to edge estimation, and, as we show later, it can be solved by similar means. The minimax convergence rates for estimators of supports with smooth boundaries turn out to be the same as those for edge estimators (cf. Chapters 4, 5).