Improvement of convergence rate in kernel density function estimation

One of the methods of probability density estimation is the kernel method. In this paper, rst, the classic kernel(CK) method is introduced. Then, in order to reduce bias, a geometric extrapolation classic kernel(GECK) method is investigated. Theoretical properties, including the selection of smoothness parameters and the accuracy of resultant estimators are studied. Accordingly, the mean integrated squared error of GECK method achieve a faster convergence rate when kernels are symmetric. In order to evaluatethe performance of this new estimator, a Monte Carlo simulation is studied. We indicate these methods by applying them to real data.

Keywords:

kernel density , convergence rate , probability , bias