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

doi:10.1016/S0167-4730(02)00008-5

2001-10-01

PRE

Pandey, MD

DOI：10.1016/S0167-4730(02)00008-5

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摘要

En 中文

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.

Keyword:

extreme values

peaks-over-threshold method

information theory

entropy

probability-weighted moments

order statistics

return period

quantile function

simulation

wind speed