A Cautionary Note on the Use of Nonparametric Bootstrap for Estimating Uncertainties in Extreme-Value Models

Abstract

The parametric and nonparametric approaches to the bootstrap are compared as to their performance in estimating uncertainties in extreme-value models. Simulation experiments make use of several combinations of true and fitted probability distributions utilized in climatological and hydrological applications. The results demonstrate that for small to moderate sample sizes the nonparametric bootstrap should be interpreted with caution because it leads to confidence intervals that are too narrow and underestimate the real uncertainties involved in the frequency models. Although the parametric bootstrap yields confidence intervals that are slightly too liberal as well, it improves the uncertainty estimates in most examined cases, even under conditions in which an incorrect parametric model is adopted for the data. Differences among three examined types of bootstrap confidence intervals (percentile, bootstrap t, and bias corrected and accelerated) are usually smaller in comparison with those between the parametric and nonparametric versions of bootstrap. It is concluded that the parametric bootstrap should be preferred whenever inferences are based on small to moderate sample sizes (n ≤ 60) and a suitable model for the data is known or can be assumed, including applications to confidence intervals related to extremes in global and regional climate model projections.