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arXiv · 1506.00878

Efficient Maximum Approximated Likelihood Inference for Tukey's g-and-h Distribution

Ganggang Xu·Marc G. Genton
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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 the 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.

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Ganggang Xu, Marc G. Genton. 2015-06-02. Efficient Maximum Approximated Likelihood Inference for Tukey's g-and-h Distribution. https://arxiv.org/abs/1506.00878

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