A simple approach to the estimation of Tukey's gh distribution. Issue 16 (1st November 2016)

• Record Type: Journal Article
• Authors: Bee, M.; Trapin, L.
• Is Part Of: Journal of statistical computation and simulation. Volume 86:Issue 16(2016)
• Page Start: 3287
• Page End: 3302
• Publication Date: 2016-11-01
• Subjects: Approximate maximum likelihood -- accept–reject algorithm -- approximate Bayesian computation -- risk measurement; 62E20 -- 62F10 -- 62F12; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5028505
• DOI: 10.1080/00949655.2016.1164159
• Languages: English
• ISSNs: 0094-9655

Abstract

ABSTRACT: The Tukey's gh distribution is widely used in situations where skewness and elongation are important features of the data. As the distribution is defined through a quantile transformation of the normal, the likelihood function cannot be written in closed form and exact maximum likelihood estimation is unfeasible. In this paper we exploit a novel approach based on a frequentist reinterpretation of Approximate Bayesian Computation for approximating the maximum likelihood estimates of the gh distribution. This method is appealing because it only requires the ability to sample the distribution. We discuss the choice of the input parameters by means of simulation experiments and provide evidence of superior performance in terms of Root-Mean-Square-Error with respect to the standard quantile estimator. Finally, we give an application to operational risk measurement.