2012/10/26 by Lepski Oleg, Oleg, Lepski
Engineering · Mathematics · #Advanced Statistical Methods and Models #Control Systems and Identification #FOS: Mathematics #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #stat.TH
paper · pdf · doi:10.48550/arxiv.1210.7078
arxiv created 2012/10/26 · openalex publication_date 2012/10/26 · arxiv updated 2012/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper deals with the density estimation on Rd under sup- norm loss. We provide with fully data-driven estimation procedure and establish for it so called sup-norm oracle inequality. The pro- posed estimator allows to take into account not only approximation properties of the underlying density but eventual independence struc- ture as well. Our results contain, as a particular case, the complete solution of the bandwidth selection problem in multivariate density model. Usefulness of the developed approach is illustrated by appli- cation to adaptive estimation over anisotropic Nikolskii classes.