New type of gamma kernel density estimator

We discuss a new kernel type estimator for density function f X ( x ) with nonnegative support. Here, we use a type of gamma density as a kernel function and modify it with expansions of exponential and logarithmic functions. Our modified gamma kernel density estimator is not only free of the boundary bias, but the variance is also in smaller orders, which are O ( n - 1 h - 1 / 4 ) in the interior and O ( n - 1 h - 3 / 4 ) in the boundary region. Furthermore, the optimal orders of its mean squared error are O ( n - 8 / 9 ) in the interior and O ( n - 8 / 11 ) in the boundary region. Simulation results that demonstrate the proposed method’s performances are also presented.