The bias reduction in density estimation using a geometric extrapolated kernel estimator

One of the nonparametric methods to estimate the probability density is kernel method. In this paper, kernel density estimation methods including the naive kernel (NK) estimator and geometric extrapolation based kernel (GEBK) method are introduced and discussed. Theoretical properties, including the selection of smoothing parameter, the accuracy of resultant estimators using Monte Carlo simulation are studied. The results show that the amount of bias in the proposed geometric extrapolation based kernel estimator significantly decreases.