Adaptive Kernel Density Estimation using Beta Kernel

Adaptive kernel estimation for unit interval compact bounded densities using beta kernel is considered. Beta kernel is an asymmetric kernel that has several particular properties such as variable kernel shapes and matching the unit interval support of the densities to be estimated. These properties make beta kernel appropriate to be used to estimate the densities considered here because of the free of boundary bias. However, the optimal fixed bandwidth beta kernel estimator is often under smoothed. In this paper, a local adaptive scheme is put forward to improve the performance of the estimator, amending smoothness at the cost of a little of optimality. The results of the simulation studies demonstrate the effectiveness of our proposal.