2020/01/29 by Sergio Brenner Miguel, Miguel, Sergio Brenner, Jan Johannes +1
Engineering · Mathematics · #62C20 (Secondary) #62G05 (Primary) 62G07 #Advanced Statistical Methods and Models #Control Systems and Identification #FOS: Mathematics #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #msc:62C20 #msc:62G05 #msc:62G07 #stat.TH
paper · pdf · doi:10.48550/arxiv.2001.10910
arxiv created 2020/01/29 · openalex publication_date 2020/01/29 · arxiv updated 2020/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study non-parametric estimation of an unknown density with support in R (respectively R+). The proposed estimation procedure is based on the projection on finite dimensional subspaces spanned by the Hermite (respectively the Laguerre) functions. The focus of this paper is to introduce a data-driven aggregation approach in order to deal with the upcoming bias-variance trade-off. Our novel procedure integrates the usual model selection method as a limit case. We show the oracle- and the minimax-optimality of the data-driven aggregated density estimator and hence its adaptivity. We present results of a simulation study which allow to compare the finite sample performance of the data-driven estimators using model selection compared to the new aggregation.