Workshop on Structure Adapting Methods - Abstract

Goldenshluger, Alexander

Selection of kernel density estimators: $bL_p$-risk oracle inequalities

We address the problem of density estimation with $bL_p$--loss by selection of kernel estimators. We propose a selection procedure and derive corresponding $bL_p$--risk oracle inequalities. The oracle inequalities lead to minimax and adaptive minimax results in a wide variety of density estimation settings. The main technical tools used in our derivations are concentration inequalities for $bL_p$--norms of empirical processes; these bounds are of interest in their own right. Joint work with O. Lepski.