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

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  • Xu, Ganggang
  • Genton, Marc G.

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.

Suggested Citation

  • Xu, Ganggang & Genton, Marc G., 2015. "Efficient maximum approximated likelihood inference for Tukey’s g-and-h distribution," Computational Statistics & Data Analysis, Elsevier, vol. 91(C), pages 78-91.
    • Handle: RePEc:eee:csdana:v:91:y:2015:i:c:p:78-91
    DOI: 10.1016/j.csda.2015.06.002
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    References listed on IDEAS

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    6. Vincenzo Verardi, 2018. "A sign and rank based semiparametrically efficient estimator for regression analysis," London Stata Conference 2018 21, Stata Users Group.

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