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Theses

Modélisation semi-paramétrique des extrêmes conditionnels

Abstract : The main goal of this thesis is to propose new estimators of the tail-index as well as the conditional extreme quantiles in a family of heavy-tailed distributions. The considered family of distributions is defined from a regression model with a location function a(·) and a scale function b(·) which are unknown. The real random variable of interest Y is simultaneously recorded with a deterministic covariate x. The residuals Z of the model are independent of the covariate and their cumulative distribution function belongs to the Fréchet domain of attraction whose the tail-index γ is unknown and assumed to be constant. For more flexibility than purely parametric approaches, we opt for a semi-parametric estimation approach. Also, the constancy of the tail-index allows us to obtain, in the case of small samples, more reliable estimates than in certain purely non-parametric approaches existing in the literature. We establish the asymptotic properties of our estimators and present some results allowing to appreciate their finite sample properties both on simulated and real data.
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Submitted on : Thursday, September 17, 2020 - 5:39:22 PM
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Aboubacrène Ag Ahmad. Modélisation semi-paramétrique des extrêmes conditionnels. Statistiques [math.ST]. Université Gaston Berger de Saint-Louis (Sénégal), 2020. Français. ⟨tel-02941714⟩

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