A Comparison of confidence intervals for generalized extreme-value distributions

Abstract

In this paper, we address the issue of the accuracy of various confidence intervals for the parameters of the generalized extreme value (GEV) distribution. In particular, we consider intervals based on two different estimates, the probability weighted moment estimates (PWM) and the optimal bounded robust estimates (OBRE). For each estimate, we evaluate both asymptotic and bootstrap intervals with data simulated from the GEV distribution. We also consider the performance of the intervals in the presence of an outlier. Our results show that the asymptotic intervals based on the OBRE generally perform well both in terms of coverage and length while those based on the PWM tend to give undercoverage in some settings and can break down in the presence of outliers. On the other hand the bootstrap intervals typically do not perform as well as the asymptotic intervals and surprisingly the bias-corrected and accelerated bootstrap intervals (BC _a ) break down in a number of cases.