Adaptive estimation of a density function using beta kernels. (8th October 2014) - Bertin, Karine; Klutchnikoff, Nicolas
<x content-type="archive" xml:space="preserve">Abstract</x> In this paper we are interested in the estimation of a density âˆ' defined on a compact interval of â„âˆ' 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 Lepskiâ€™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.