##Statistics Seminar##\\ Department of Mathematical Sciences
~~META:title =September 10, 2015~~
^ **DATE:**|Thursday, March 3, 2016 |
^ **TIME:**|1:15pm to 2:15pm |
^ **LOCATION:**|WH 100E |
^ **SPEAKER:**|Ganggang Xu, Binghamton University |
^ **TITLE:**|Efficient Maximum Approximated Likelihood Inference for Tukey's g-and-h Distribution|
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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.