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.

A common statistical problem in hydrology is the estimation of annual maximal river flow distributions and their quantiles, with the objective of evaluating flood protection systems. Typically, record lengths are short and estimators imprecise, so that it is advisable to exploit additional sources of information. However, there is often uncertainty about the adequacy of such information, and a strict decision on whether to use it is difficult. We propose penalized quasi-maximum likelihood estimators to overcome this dilemma, allowing one to push the model towards a reasonable direction defined a priori. We are particularly interested in regional settings, with river flow observations collected at multiple stations. To account for regional information, we introduce a penalization term inspired by the popular Index Flood assumption. Unlike in standard approaches, the degree of regionalization can be controlled gradually instead of deciding between a local or a regional estimator. Theoretical results on the consistency of the estimator are provided and extensive simulations are performed for the reason of comparison with other local and regional estimators. The proposed procedure yields very good results, both for homogeneous as well as for heterogeneous groups of sites. A case study consisting of sites in Saxony, Germany, illustrates the applicability to real data.

In environmental sciences, it is often of interest to assess whether the dependence between extreme measurements has changed during the observation period. The aim of this work is to propose a statistical test that is particularly sensitive to such changes. The resulting procedure is also extended to allow the detection of changes in the extreme-value dependence under the presence of known breaks in the marginal distributions. Simulations are carried out to study the finite-sample behavior of both versions of the proposed test. Illustrations on hydrological data sets conclude the work.

This article deals with the right-tail behavior of a response distribution F Y conditional on a regressor vector X " x restricted to the heavy-tailed case of Pareto-type conditional distributions F Y py| xq " P pY ď y| X " xq, with heaviness of the right tail characterized by the conditional extreme value index γpxq ą 0. We particularly focus on testing the hypothesis H 0,tail : γpxq " γ 0 of constant tail behavior for some γ 0 ą 0 and all possible x. When considering x as a time index, the term trend analysis is commonly used. In the recent past several such trend analyses in extreme value data have been published, mostly focusing on time-varying modeling of location and scale parameters of the response distribution. In many such environmental studies a simple test against trend based on Kendall's tau statistic is applied. This test is powerful when the center of the conditional distribution F Y py|xq changes monotonically in x, for instance, in a simple location model µpxq " µ 0`x¨µ1 , x " p1, xq 1 , but the test is rather insensitive against monotonic tail behavior, say, γpxq " η 0`x¨η1 . This has to be considered, since for many environmental applications the main interest is on the tail rather than the center of a distribution. Our work is motivated by this problem and it is our goal to demonstrate the opportunities and the limits of detecting and estimating non-constant conditional heavy-tail behavior with regard to applications from hydrology. We present and compare four different procedures by simulations and illustrate our findings on real data from hydrology: Weekly maxima of hourly precipitation from France and monthly maximal river flows from Germany.

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