Abstract
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.
Highlights
The modeling of extreme events arises in many fields such as finance, insurance or environmental science
A recurrent statistical problem is the estimation of extreme quantiles associated with a random variable Y, see the reference books [1, 13, 24]
Semi-parametric methods have been considered for trend modeling in extreme events [10, 27]: A nonparametric regression model of the trend is combined with a parametric model for extreme values
Summary
The modeling of extreme events arises in many fields such as finance, insurance or environmental science. Without additional assumptions on the pair (Y, x), the estimation of extreme conditional quantiles is addressed using nonparametric methods, see for instance the recent works of [9, 19, 21] These methods may suffer from the curse of dimensionality which is compounded in distribution tails by the fact that observations are rare by definition. We assume that the response variable and the covariate are linked by a location-dispersion regression model Y = a(x) + b(x)Z, see [39], where Z is a heavy-tailed random variable This model is flexible since (i) no parametric assumptions are made on a(·), b(·) and Z, (ii) it allows for heteroscedasticity via the function b(·).
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