Bias reductions for beta kernel estimation

The beta kernel estimator for a density with support was discussed by Chen [(1999) ‘Beta Kernel Estimators for Density Functions’, Computational Statistics and Data Analysis, 31, 131–145]. In this paper, when the underlying density has a fourth-order derivative, we improve the beta kernel estimator using the bias correction techniques based on two beta kernel estimators with different smoothing parameters. As a result, we propose new bias corrected beta kernel estimators involving the digamma functions, and then establish their asymptotic properties. Simulation studies are conducted to illustrate the finite sample performance of the proposed estimators.