The Relative Improvement of Bias Reduction in Density Estimator Using Geometric Extrapolated Kernel

One of a nonparametric procedures used to estimate densities is kernel method. In this paper, in order to reduce bias of  kernel density estimation, methods such as usual kernel(UK), geometric extrapolation usual kernel(GEUK), a bias reduction kernel(BRK) and a geometric extrapolation bias reduction kernel(GEBRK) are introduced. Theoretical properties, including the selection of smoothness parameter and the accuracy of resultant estimators are studied. Accordingly, the mean integrated squared error of GEBRK method achieve a faster convergence rate when kernels are symmetric, where n is the sample size. In order to evaluate the performance of these new estimators, we conduct a Monte Carlo simulation study. The obtained results are illustrated by analyzing real data. The results show that the amount of bias in the proposed BRK and GEBRK methods significantly decreases../files/site1/files/42/7Abstract.pdf