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Efficient maximum approximated likelihood inference for Tukey’s g-and-h distribution
Ist Teil von
Computational statistics & data analysis, 2015-11, Vol.91, p.78-91
Ort / Verlag
Elsevier B.V
Erscheinungsjahr
2015
Link zum Volltext
Quelle
Alma/SFX Local Collection
Beschreibungen/Notizen
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.