Non compact estimation of the conditional density from direct or noisy data

Abstract

. In this paper, we propose a nonparametric estimation strategy for the conditional density function of Y given X , from independent and identically distributed observations ( X i , Y i ) 1 ≤ i ≤ n . We consider a regression strategy related to projection subspaces of L 2 generated by non compactly supported bases. This (cid:28)rst study is then extended to the case where Y is not directly observed, but only Z = Y + ε , where ε is a noise with known density. In these two settings, we build and study collections of estimators, compute their rates of convergence on anisotropic space on non-compact supports, and prove related lower bounds. Then, we consider adaptive estimators for which we also prove risk bounds.