Optimisation of Smoothing Parameter of Diffeomorphism Kernel Estimate for Bounded Random Data

摘要

The Diffeomorphism Kernel Density Estimator (DKDE) requires the estimation of an optimal value of the bandwidth to ensure a reliable pdf estimation of bounded distributions. In this paper, we suggest to approach the optimal bandwidth value by adapting Plug-in algorithm to DKDE estimator. We will show that the proposal method allows better density estimation in the MISE sense. Otherwise, the Gibbs phenomenon completely disappears. These results are illustrated by some bounded and semi bounded distributions simulations.