ESAIM: Probability and Statistics

Table of Contents - 2012 - Volume 16  

Research Article

Adaptive non-asymptotic confidence balls in density estimation

Matthieu Lerasle

Institut de Mathématiques (UMR 5219), INSA de Toulouse, Université de Toulouse, France. lerasle@gmail.com

Abstract

We build confidence balls for the common density s of a real valued sample X1,...,Xn. We use resampling methods to estimate the projection of s onto finite dimensional linear spaces and a model selection procedure to choose an optimal approximation space. The covering property is ensured for all n ≥ 2 and the balls are adaptive over a collection of linear spaces.

(Received November 14 2008)

(Revised January 11 2010)

(Online publication July 02 2012)

Key Words:

  • Confidence balls;
  • density estimation;
  • resampling methods

Mathematics Subject Classification:

  • 62G07;
  • 62G09;
  • 62G10;
  • 62G15