Adaptive estimation of a density function using beta kernels. (8th October 2014)

• Record Type: Journal Article
• Authors: Bertin, Karine; Klutchnikoff, Nicolas
• Is Part Of: ESAIM. Volume 18(2014)
• Page Start: 400
• Page End: 417
• Publication Date: 2014-10-08
• Subjects: Beta kernels, -- adaptive estimation, -- minimax rates, -- Hölder spaces; Probabilities -- Periodicals; Mathematical statistics -- Periodicals; 519.2
• DOI: 10.1051/ps/2014010
• Languages: English
• ISSNs: 1292-8100

Abstract

Abstract : In this paper we are interested in the estimation of a density − defined on a compact interval of ℝ− from n independent and identically distributed observations. In order to avoid boundary effect, beta kernel estimators are used and we propose a procedure (inspired by Lepski's method) in order to select the bandwidth. Our procedure is proved to be adaptive in an asymptotically minimax framework. Our estimator is compared with both the cross-validation algorithm and the oracle estimator using simulated data.