Efficient maximum approximated likelihood inference for Tukey's g-and-h distribution

Abstract
Abstract Tukey's g-and-h distribution has been a powerful tool for data exploration and modeling since its introduction. However, two long standing challenges associated with this distribution family have remained unsolved until this day: how to find an optimal estimation procedure and how to make valid statistical inference on unknown parameters. To overcome these two challenges, a computationally efficient estimation procedure based on maximizing an approximated likelihood function of Tukey's g-and-h distribution is proposed and is shown to have the same estimation efficiency as the maximum likelihood estimator under mild conditions. The asymptotic distribution of the proposed estimator is derived and a series of approximated likelihood ratio test statistics are developed to conduct hypothesis tests involving two shape parameters of Tukey's g-and-h distribution. Simulation examples and an analysis of air pollution data are used to demonstrate the effectiveness of the proposed estimation and testing procedures.

Citation
Xu, G., & Genton, M. G. (2015). Efficient maximum approximated likelihood inference for Tukey’s g-and-h distribution. Computational Statistics & Data Analysis, 91, 78–91. doi:10.1016/j.csda.2015.06.002

Publisher
Elsevier BV

Journal
COMPUTATIONAL STATISTICS & DATA ANALYSIS

DOI
10.1016/j.csda.2015.06.002

Additional Links
https://linkinghub.elsevier.com/retrieve/pii/S0167947315001401

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