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Discipline of Business Analaytics

Family of Generalized Gamma Kernels: A Unified Approach to the Asymptotics on Asymmetric Kernels

Professor Masayuki Hirukawa, Faculty of Economics; Setsunan University

1st Mar 2013  11:00 am - Room 498

Unlike symmetric kernels, exploiting the asymptotics on asymmetric kernels has relied on kernel-specific arguments. Toward a unified approach to their asymptotics, this paper proposes a generic form of asymmetric kernels that consists of a set of common conditions. The generic kernel, called a family of Generalized Gamma kernels, is built on the Generalized Gamma density function, and incorporates the Modified Gamma kernel as a special case. As other special cases, two new kernels, namely, the Weibull and Nakagami-m kernels, are also proposed. The density estimator using Generalized Gamma kernels is shown to preserve the appealing properties that the Gamma and Modified Gamma kernels possess. Furthermore, this paper investigates three extensions of the density estimation including multiplicative bias correction.