We consider estimating density functions which have support on [0, ∞) 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 non-negative 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 x 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.
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Chen, S.X. Probability Density Function Estimation Using Gamma Kernels. Annals of the Institute of Statistical Mathematics 52, 471–480 (2000). https://doi.org/10.1023/A:1004165218295
- Boundary bias
- gamma kernels
- local linear estimators
- variable kernels