TITLE:
Some Improvement on Convergence Rates of Kernel Density Estimator
AUTHORS:
Xiaoran Xie, Jingjing Wu
KEYWORDS:
Kernel Density Estimation, Geometric Extrapolation, Bias Reduction, Mean Squared Error, Convergence Rate
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.11,
June
20,
2014
ABSTRACT: In this paper two
kernel density estimators are introduced and investigated. In order to reduce
bias, we intuitively subtract an estimated bias term from ordinary kernel
density estimator. The second proposed density estimator is a geometric
extrapolation of the first bias reduced estimator. Theoretical properties such
as bias, variance and mean squared error are investigated for both estimators.
To observe their finite sample performance, a Monte Carlo simulation study
based on small to moderately large samples is presented.