Efficient Maximum Approximated Likelihood Inference for Tukey's g-and-h Distribution
Abstract
Tukey's -and- 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 -and- 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 -and- distribution. Simulation examples and an analysis of air pollution data are used to demonstrate the effectiveness of the proposed estimation and testing procedures.
Cite
@article{arxiv.1506.00878,
title = {Efficient Maximum Approximated Likelihood Inference for Tukey's g-and-h Distribution},
author = {Ganggang Xu and Marc G. Genton},
journal= {arXiv preprint arXiv:1506.00878},
year = {2015}
}