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Modeling the dependence of pre-asymptotic extremes

Abstract : In various applications in environmental sciences, finance, insurance or risk management, joint extremal behavior between random variables is of particular interest. For example, this plays a central role in assessing risks of natural disasters. Misspecification of the dependence between random variables can lead to substantial underestimation of risk, especially at extreme levels. This thesis develops inference techniques for Archimax copulas. These copula models can account for any type of asymptotic dependence between extremes and at the same time capture joint risks at medium levels. An Archimax copula is characterized by two functional parameters, the stable tail dependence function (stdf), and the Archimedean generator which acts as a distortion of the extreme-value dependence model. Conditions under which the generator and the stdf are identifiable are derived so that a semiparametric approach for inference can be developed. Two nonparametric estimators of the stdf and a moment-based estimator of the generator, which assumes that the latter belongs to a parametric family, are proposed. The asymptotic behavior of the estimators is then established under broad regularity conditions; performance in small samples is assessed through a comprehensive simulation study. In the second part of the thesis, Archimax copulas are generalized to a clustered constructions in order to bring in more flexibility, which is needed in practical applications. The extremal behavior of this new dependence model is derived herein. Finally, the methodology proposed herein is illustrated on precipitation data. First, a trivariate Archimax copula is used to analyze monthly rainfall maxima at three stations in French Brittany. The model is seen to fit the data very well, both in the lower and in the upper tail. The nonparametric estimator of the stdf reveals asymmetric extremal dependence between the stations, which reflects heavy precipitation patterns in the area. An application of the clustered Archimax model to a precipitation dataset containing 155 stations is then presented, where groups of asymptotically dependent stations are determined via a specifically tailored clustering algorithm. Finally, possible ways to model inter cluster dependence are discussed
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Submitted on : Friday, February 14, 2020 - 10:43:20 AM
Last modification on : Saturday, March 7, 2020 - 4:52:58 AM


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  • HAL Id : tel-02478874, version 1


Simon Chatelain. Modeling the dependence of pre-asymptotic extremes. Statistics [math.ST]. Université de Lyon; McGill university (Montréal, Canada), 2019. English. ⟨NNT : 2019LYSE1267⟩. ⟨tel-02478874⟩



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