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Adaptive estimation of a density function using beta kernels
Published online by Cambridge University Press: 08 October 2014
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.
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- © EDP Sciences, SMAI 2014
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