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.