Adaptive Bayesian bandwidth selection in asymmetric kernel density estimation for nonnegative heavy-tailed data

Abstract

In this paper, we consider an interesting problem on adaptive Birnbaum–Saunders-power-exponential (BS-PE) kernel density estimation for nonnegative heavy-tailed (HT) data. Treating the variable bandwidths , of adaptive BS-PE kernel as parameters, we then propose a conjugate prior and estimate the 's by using the popular quadratic and entropy loss functions. Explicit formulas are obtained for the posterior and Bayes estimators. Comparison simulations with global unbiased cross-validation bandwidth selection technique were conducted under four HT distributions. Finally, two applications based on HT real data are presented and analyzed.