Multiplicative bias correction for inverse gamma and beta prime kernel density estimators

Abstract

In this paper, we demonstrate that the multiplicative bias correction (MBC) approaches can be extended for both Inverse Gamma (IG) and Beta Prime (BP) kernel density estimators. First, some properties of the MBC-IG and MBC-BP kernel density estimators (bias, variance and mean integrated squared error) are shown. Second, the least square cross validation technique (LSCV) is adapted for the choice of bandwidth. Finally, the performances of the MBC estimators based on IG and BP kernels are illustrated by two studies, a simulation study, followed by a real application study with positive support. In general, in terms of the two criterions, integrated squared bias (ISB) and integrated squared error (ISE), the proposed estimators outperform the classical IG and BP kernel estimators.

Keywords:

• Bandwidth
• Beta prime kernel
• Inverse gamma kernel
• Multiplicative bias correction
• Positive data