Statistics and Its Interface
Volume 7 (2014)
Special Issue on Extreme Theory and Application (Part I)
Guest Editors: Yazhen Wang and Zhengjun Zhang
Point and exact interval estimation for the generalized Pareto distribution with small samples
Pages: 389 – 404
In extreme value theory, the generalized Pareto distribution (GPD) is used to model another distribution on the tail. Since only a proportion of the data is used, the effective data size for fitting GPD is often small. As statistical properties, especially tail behaviour, of GPD largely depend on its shape parameter, performances of most existing methods are inconsistent when the value of the shape parameter varies. In this paper, we introduce a new method to fit GPD that improves the performance over existing methods for very small samples, in terms of bias and mean square error as well as confidence intervals. The numerical study in this paper also shows that better performance on parameter estimation does not necessarily lead to better performance on quantile estimation.
confidence interval, extreme value theory, generalized Pareto distribution, quantile, shape parameter, small sample