Minimum cross-entropy method for extreme value estimation using peaks-over-threshold data

Extreme quantile estimation in the peaks-over-threshold (POT) method is based on the Pareto distribution model for peaks of a time series exceeding a high threshold. However, a major practical difficulty associated with this approach is the large and erratic variability of quantile estimates with respect to the threshold value, which is not known a priori. Recognizing the limited applicability of the Pareto model to a narrow and unidentifiable range of peak data, the paper presents a more general non-parametric probabilistic model to improve the statistical accuracy and of POT estimates. The proposed approach relies on a quantitative notion of uncertainty and the minimum cross-entropy principle (Cross-Ent), commonly used in information theory and signal analysis. The model combine a suitable prior distribution with sample estimates of probability-weighted-moments, which exhibit much smaller sampling uncertainty than estimates of ordinary moments. The performance of the Cross-Ent approach is compared with a widely used Pareto model of peak data and an exponential model of transformed data. Examples based on simulated data illustrate that Cross-Ent estimates of 50 and 1000-year quantiles are almost unbiased and insensitive to the threshold value. The analysis of US wind speed data also reveals a remarkably stable trend of Cross-Ent estimates with very limited threshold sensitivity, which is in clear contrast with rapidly fluctuating estimates obtained from the other two methods. (C) 2002 Elsevier Science Ltd. All rights reserved.