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Regional extreme value index estimation and a test of tail homogeneity
Author(s) -
Kinsvater Paul,
Fried Roland,
Lilienthal Jona
Publication year - 2016
Publication title -
environmetrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.68
H-Index - 58
eISSN - 1099-095X
pISSN - 1180-4009
DOI - 10.1002/env.2376
Subject(s) - extreme value theory , generalized pareto distribution , estimator , pairwise comparison , econometrics , generalized extreme value distribution , homogeneity (statistics) , statistics , univariate , inference , mathematics , index (typography) , multivariate statistics , computer science , artificial intelligence , world wide web
This paper deals with inference on extremes of heavy‐tailed distributions. We assume distribution functions F of Pareto‐type, where the right‐tail behavior of F is characterized by a strictly positive parameter γ , the so‐called extreme value index (EVI). In some applications, observations from closely related variables are available, with possibly identical EVI γ . If these variables are observed for the same time period, a procedure called BEAR estimator has recently been proposed. We modify this approach allowing for different observation periods and pairwise extreme value dependence of the variables. In addition, we present a new test for equality of the EVI. As an application, we discuss regional flood frequency analysis, where we want to combine rather short sequences of univariate observations with very different lengths measured at many gauges for joint inference. We illustrate our findings on peak discharges from 18 river gauges located at the Mulde basin in Germany, which is known for its severe summer floods, and identify relevant heterogeneous tail behavior, which is not detected by other popular methods. Copyright © 2015 John Wiley & Sons, Ltd.