The adaptive gamma-BSPE kernel density estimation for nonnegative heavy-tailed data

Abstract

In this work, we consider the nonparametric estimation of the probability density function for nonnegative heavy-tailed (HT) data. The objective is first to propose a new estimator that will combine two regions of observations (high and low density). While associating a gamma kernel to the high-density region and a BS-PE kernel to the low-density region. Then, to compare the proposed estimator with the classical estimator in order to evaluate its performance. The choice of bandwidth is investigated by adopting the popular cross-validation technique and two variants of the Bayesian approach. Finally, the performances of the proposed and the classical estimators are illustrated by a simulation study and real data.

Keywords

• Bayesian bandwidth selector
• BS-PE kernel
• Cross validation
• Gamma kernel
• Heavy tailed data
• MCMC method