Data-driven aggregation in non-parametric density estimation on the real line

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-driv...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2020-01
Main Authors: Sergio Brenner Miguel, Johannes, Jan
Format: Article
Language:English
Subjects:
Agglomeration
Computer simulation
Density
Economic models
Minimax technique
Parameter estimation
Subspaces
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2331-8422