Title: Estimator Selection: a New Method with Applications to Kernel Density Estimation

Author(s): Claire Lacour, Pascal Massart and Vincent Rivoirard
Issue: Volume 79 Series A Part 2 Year 2017
Pages: 298 -- 335
Estimator selection has become a crucial issue in non parametric estimation. Two widely used methods are penalized empirical risk minimization (such as penalized log-likelihood estimation) or pairwise comparison (such as Lepski’s method). Our aim in this paper is twofold. First we explain some general ideas about the calibration issue of estimator selection methods. We review some known results, putting the emphasis on the concept of minimal penalty which is helpful to design data-driven selection criteria. Secondly we present a new method for bandwidth selection within the framework of kernel density density estimation which is in some sense intermediate between these two main methods mentioned above. We provide some theoretical results which lead to some fully data-driven selection strategy.
AMS (2000) subject classification. Primary: 62G05; Secondary: 62C20, 62H12.
Keywords and phrases: Concentration inequalities, Kernel density estimation, Penalization methods, Estimator selection, Oracle inequality.