Coverage probability of bootstrap confidence intervals in heavy-tailed frequency models, with application to precipitation data

Abstract

Bootstrap, a technique for determining the accuracy of statistics, is a tool widely used in climatological and hydrological applications. The paper compares coverage probabilities of confidence intervals of high quantiles (5- to 200-year return values) constructed by the nonparametric and parametric bootstrap in frequency analysis of heavy-tailed data, typical for maxima of precipitation amounts. The simulation experiments are based on a wide range of models used for precipitation extremes (generalized extreme value, generalized Pareto, generalized logistic, and mixed distributions). The coverage probability of the confidence intervals is quantified for several sample sizes (n = 20, 40, 60, and 100) and tail behaviors. We show that both bootstrap methods underestimate the width of the confidence intervals but that the parametric bootstrap is clearly superior to the nonparametric one. Even a misspecification of the parametric model—often unavoidable in practice—does not prevent the parametric bootstrap from performing better in most cases. A tendency to narrower confidence intervals from the nonparametric than parametric bootstrap is demonstrated in the application to high quantiles of distributions of observed maxima of 1- and 5-day precipitation amounts; the differences increase with the return level. The results show that estimation of uncertainty based on nonparametric bootstrap is highly unreliable, especially for small and moderate sample sizes and for very heavy-tailed data.