A0921
Title: Interval estimation and hypothesis testing for the generalized Pareto distribution under non-regularity conditions
Authors: Hideki Nagatsuka - Chuo University (Japan) [presenting]
Narayanaswamy Balakrishnan - McMaster University (Canada)
Abstract: The generalized Pareto distribution (GPD), introduced by Pickands, is widely used to model exceedances over thresholds. It is well known that inference for the GPD is a difficult problem since the moments exist only for a limited range of parameters and the GPD violates the classical regularity conditions in the maximum likelihood method. For parameter estimation, most existing methods do not perform satisfactorily for all ranges of parameters. Furthermore, the interval estimation and hypothesis tests have not been studied well in the literature. We introduce a novel framework for inference for the GPD, which works successfully for all values of the shape parameter. Specifically, a new method of parameter estimation for the GPD is constructed, and some asymptotic properties of the proposed estimators and related statistics are derived. The existence and uniqueness of the proposed estimates are also established. Based on the asymptotic properties of the proposed estimators and related statistics, new confidence intervals and hypothesis tests are developed. The performances of the proposed estimators of parameters, confidence intervals and hypothesis tests are then shown by Monte Carlo simulation and real data examples.