Statistics of Heteroscedastic Extremes

Einmahl, J.H.J.; Haan, Leo de; Zhou, Chen

doi:10.1111/rssb.12099

Cited by 87 publications

(141 citation statements)

References 18 publications

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“…The estimation of γ (x 0 ) has been addressed by many authors such as Smith (1990), Smith (1989), and Chavez-Demoulin and Davison (2005). Einmahl et al (2014) consider the case where survival functions S x 1 (·), . .…”

Section: Introductionmentioning

confidence: 99%

A general estimator for the extreme value index: applications to conditional and heteroscedastic extremes

Gardès

2015

Extremes

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The tail behavior of a survival function is controlled by the extreme value index. The aim of this paper is to propose a general procedure for the estimation of this parameter in the case where the observations are not necessarily distributed from the same distribution. The idea is to estimate in a consistent way the survival function and to apply a general functional to obtain a consistent estimator for the extreme value index. This procedure permits to deal with a large set of models such as conditional extremes and heteroscedastic extremes. The consistency of the obtained estimator is established under general conditions. A simulation study and a concrete application on financial data are proposed to illustrate the finite sample behavior of the proposed procedure.

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Section: Introductionmentioning

confidence: 99%

A general estimator for the extreme value index: applications to conditional and heteroscedastic extremes

Gardès

2015

Extremes

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“…Of course time series of daily temperatures are neither independent (they are somewhat autocorrelated) nor identically distributed (their distributions vary within a year). There is however theoretical justification for the use of GEV distributions in our case: it has been shown that the independence assumption can be relaxed for weakly dependent stationary time series (Leadbetter et al, 1983;Hsing, 1991), and Einmahl et al (2016) extended the theory to non-identically distributed observations with conditions on the tail distributions (e.g., distributions share a common absolute maximum). In this work, we explicitly assess whether inferred GEV distributions actually provide an adequate description of the data set in question.…”

Section: Statistical Backgroundmentioning

confidence: 99%

Estimating changes in temperature extremes from millennial-scale climate simulations using generalized extreme value (GEV) distributions

Huang

Stein

McInerney

et al. 2016

Adv. Stat. Clim. Meteorol. Oceanogr.

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Abstract. Changes in extreme weather may produce some of the largest societal impacts of anthropogenic climate change. However, it is intrinsically difficult to estimate changes in extreme events from the short observational record. In this work we use millennial runs from the Community Climate System Model version 3 (CCSM3) in equilibrated pre-industrial and possible future (700 and 1400 ppm CO 2 ) conditions to examine both how extremes change in this model and how well these changes can be estimated as a function of run length. We estimate changes to distributions of future temperature extremes (annual minima and annual maxima) in the contiguous United States by fitting generalized extreme value (GEV) distributions. Using 1000-year pre-industrial and future time series, we show that warm extremes largely change in accordance with mean shifts in the distribution of summertime temperatures. Cold extremes warm more than mean shifts in the distribution of wintertime temperatures, but changes in GEV location parameters are generally well explained by the combination of mean shifts and reduced wintertime temperature variability. For cold extremes at inland locations, return levels at long recurrence intervals show additional effects related to changes in the spread and shape of GEV distributions. We then examine uncertainties that result from using shorter model runs. In theory, the GEV distribution can allow prediction of infrequent events using time series shorter than the recurrence interval of those events. To investigate how well this approach works in practice, we estimate 20-, 50-, and 100-year extreme events using segments of varying lengths. We find that even using GEV distributions, time series of comparable or shorter length than the return period of interest can lead to very poor estimates. These results suggest caution when attempting to use short observational time series or model runs to infer infrequent extremes.

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“…However, in the previous references it assumed that the observations are identically distributed. Recently, Einmahl et al [2016] showed consistency of classical tail estimators under slightly weaker assumptions called heteroscedastic extremes, but still they need that the tail behavior, i.e., the extreme value index γ is the same for all observations. In analogy to the previous subsection, we first check whether the extreme value index of monthly maximal flows is constant over the whole observation period.…”

Section: Monthly Maximal Flows At the Mulde River Basin In Germanymentioning

confidence: 99%

“…For many environmental applications the main interest is in the frequency of hazardous events, e.g., extreme precipitations and floods. Accordingly, there is a number of articles introducing methodology for change-points [Jarušková and Rencová, 2008;Kim and Lee, 2009;Dierckx and Teugels, 2010;Dupuis et al, 2015;Bücher et al, 2015;Kojadinovic and Naveau, 2015] and regression/trend analysis [Chavez-Demoulin and Davison, 2005;Wang and Tsai, 2009;Gardes and Girard, 2010;Dierckx, 2011;Wang et al, 2012;Wang and Li, 2013;Einmahl et al, 2016;de Haan et al, 2015] of extremes, just to name a few recent contributions. For a case study and an overview of many flood trend analyses we refer to Mediero et al [2014].…”

Section: Introductionmentioning

confidence: 99%

Conditional heavy-tail behavior with applications to precipitation and river flow extremes

Kinsvater

Fried

2016

Stoch Environ Res Risk Assess

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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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Statistics of Heteroscedastic Extremes

Cited by 87 publications

References 18 publications

A general estimator for the extreme value index: applications to conditional and heteroscedastic extremes

A general estimator for the extreme value index: applications to conditional and heteroscedastic extremes

Estimating changes in temperature extremes from millennial-scale climate simulations using generalized extreme value (GEV) distributions

Conditional heavy-tail behavior with applications to precipitation and river flow extremes

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