Probability density function estimation using gamma kernels

We consider estimating density functions which have support on [0, infinity) using some gamma probability densities as kernels to replace the fixed and symmetric kernel used in the standard kernel density estimator. The gamma kernels are nonnegative and have naturally varying shape. The gamma kernel estimators are free of boundary bias, non-negative and achieve the optimal rate of convergence for the mean integrated squared error. The variance of the gamma kernel estimators at a distance a: away from the origin is O(n(-4/5)x(-1/2)) indicating a smaller variance as x increases. Finite sample comparisons with other boundary bias free kernel estimators are made via simulation to evaluate the performance of the gamma kernel estimators.