Estimation of Tukey G - and - H Distributional Family Parameters by Quantile Least Squares Method

• Activity Number: 133
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Biopharmaceutical Section
• Author(s): Yihuan Xu*+ and Boris Iglewicz
• Companies: ImClone Systems, a wholly-owned subsidiary of Eli Lilly and Company and Temple University
• Keywords: Tukey g - and - h distribution ; Robust ; Quantiles ; Least squares

Abstract

The Tukey g - and - h distributional family is generated from a relatively simple transformation of the standard normal and can approximate a broad spectrum of distributions. Thus, it is easy to use in simulation studies and has been applied in multiple areas. We propose a quantile based least squares (QLS) estimation method to fit the Tukey g - and - h distributional family parameters and extend the method to a robust version. Basic properties of the QLS method are derived and comparisons made with competing methods through simulation. Several real microarray data examples are used as illustrations.