caa a22 4500 47582671X CHVBK 20180406123830.0 cr unu---uuuuu 170329e20000901xx s 000 0 eng 10.1023/A:1004165218295 doi (NATIONALLICENCE)springer-10.1023/A:1004165218295 Chen Song Department of Statistical Science, La Trobe University, 3083, Victoria, Australia aut Probability Density Function Estimation Using Gamma Kernels [Elektronische Daten] [Song Chen] 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. The Institute of Statistical Mathematics, 2000 Boundary bias nationallicence gamma kernels nationallicence local linear estimators nationallicence variable kernels nationallicence Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 52/3(2000-09-01), 471-480 0020-3157 52:3<471 2000 52 10463 https://doi.org/10.1023/A:1004165218295 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1004165218295 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Chen Song Department of Statistical Science, La Trobe University, 3083, Victoria, Australia aut NATIONALLICENCE 773 0- Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 52/3(2000-09-01), 471-480 0020-3157 52:3<471 2000 52 10463 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer