Improved Small Sample Inference for the Generalized Pareto Distribution Through a Monte Carlo Adjustment to the Signed Root of the Log-Likelihood Ratio Statistic

• Activity Number: 643
• Type: Contributed
• Date/Time: Thursday, August 7, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): David Smith*+
• Companies: Tennessee Tech University
• Keywords: Generalized Pareto distribution ; inference ; log-likelihood ratio statistic ; confidence intervals ; small samples

Abstract

Estimation methods for the Generalized Pareto distribution have been well studied. While the maximum likelihood method may yield adequate results for cases in which the shape parameter falls between -.5 to 5 and large sample sizes, very little has been done for small sample sizes. Small sample sizes can occur when fitting the exceedance over a threshold. We study an adjustment which centers and scales the signed root of the log-likelihood ratio statistic. The Monte Carlo adjustment is easily derived and does not require complex calculations that are often required to condition on ancillary statistics. One-sided inference and confidence intervals for shape, scale, and m-year return levels are compared to profile likelihood and delta methods. Considerable improvement is shown for small samples and demonstrated with examples.