Family of the generalised gamma kernels: a generator of asymmetric kernels for nonnegative data

Masayuki Hirukawa and Mari Sakudo

Journal of Nonparametric Statistics, 2015, vol. 27, issue 1, 41-63

Abstract: Unlike symmetric kernels, so far exploring asymptotics on asymmetric kernels has relied on diversified approaches. This paper proposes a family of the generalised gamma (GG) kernels that is built on the probability density function of the GG distribution [Stacy, E.W. (1962), 'A Generalization of the Gamma Distribution', Annals of Mathematical Statistics , 33, 1187-1192] and a few common conditions. The family can generate asymmetric kernels that share appealing properties with the modified gamma kernel [Chen, S.X. (2000), 'Probability Density Function Estimation Using Gamma Kernels', Annals of the Institute of Statistical Mathematics , 52, 471-480]. Asymptotics on the kernels generated from the family can be delivered by manipulating the conditions directly, as with symmetric kernels.

Date: 2015
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DOI: 10.1080/10485252.2014.998669

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