Multiplicative bias correction for generalized Birnbaum–Saunders kernel density estimators and application to nonnegative heavy tailed data

Abstract

In this paper, we show that the multiplicative bias correction (MBC) techniques can be applied for generalized Birnbaum–Saunders (GBS) kernel density estimators. First, some properties of the MBC-GBS kernel density estimators (bias, variance and mean integrated squared error) are shown. Second, the choice of bandwidth is investigated by adopting the popular cross-validation technique. Finally, the performances of the MBC estimators based on GBS kernels are illustrated by a simulation study, followed by a real application for nonnegative heavy tailed (HT) data. In general, in terms of integrated squared bias (ISB) and integrated squared error (ISE), the proposed estimators outperform the standard GBS kernel estimators.