Estimation of extreme quantiles from heavy-tailed distributions in a location-dispersion regression model

We consider a location-dispersion regression model for heavy-tailed distributions when the multidimensional covariate is deterministic. In a first step, nonparametric estimators of the regression and dispersion functions are introduced. This permits, in a second step, to derive an estimator of the c...

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Bibliographic Details
Published inElectronic journal of statistics Vol. 14; no. 2; pp. 4421 - 4456
Main Authors Ahmad, Aboubacrène Ag, Deme, El Hadji, Diop, Aliou, Girard, Stéphane, Usseglio-Carleve, Antoine
Format Journal Article
LanguageEnglish
Published Shaker Heights, OH : Institute of Mathematical Statistics 01.01.2020
Subjects
Mathematics
Statistics
Semi-parametric estimation
Extreme conditional quantile
Tail-index
Regression and dispersion functions
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Summary:We consider a location-dispersion regression model for heavy-tailed distributions when the multidimensional covariate is deterministic. In a first step, nonparametric estimators of the regression and dispersion functions are introduced. This permits, in a second step, to derive an estimator of the conditional extreme-value index computed on the residuals. Finally, a plug-in estimator of extreme conditional quantiles is built using these two preliminary steps. It is shown that the resulting semi-parametric estimator is asymptotically Gaussian and may benefit from the same rate of convergence as in the unconditional situation. Its finite sample properties are illustrated both on simulated and real tsunami data.
ISSN:1935-7524
1935-7524
DOI:10.1214/20-EJS1779