Extreme values study with high-dimensional covariate

Abstract : The aim of the thesis is to study some estimators of extreme conditional quantiles by using the inversion method of associated survival function local estimators. These estimators depend on weights function whose role is to select the more relevant covariates in a sample. In a first chapter, we establish the asymptotic normality of these estimators. It requires a new condition on the distribution of interest which is called Tail First Order condition. This condition is satisfied by distributions verifying the Gnedenko-Fisher-Tippet theorem but also by super heavy-tailed distributions. Other classical conditions are necessary, in particular about the nature of the quantile which has to be intermediate. In a second chapter, we define by extrapolation a new extreme quantile estimator and we prove the consistency. The curse of dimensionality problem is also discussed. In both chapters, some particular cases are studied as the well known Nadaraya-Watson estimator or nearest neighbors estimator. The perfomances of the different estimators are tested with simulation study. An application to real data set has been done too.
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Claire Roman. Extreme values study with high-dimensional covariate. Statistics [stat]. UMR 7501, 2019. English. ⟨tel-02278367⟩

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