Smoothed bootstrapping kernel density estimation under higher order kernel

Abstract

Smoothed bootstrap method is a useful method to approximates the bias of Kernel density estimation. However, it can only be applied when the kernel function is of second order. In this study, we propose a novel method to generalize the smoothed bootstrap method to higher order kernel for estimating the bias and construct bias corrected estimator based on it. Theoretical formulation and numerical simulation demonstrate that the proposed method achieve better performance compared to the traditional bias correction method.