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Estimation of extreme quantiles from heavy-tailed distributions in a location-dispersion regression model. (English) Zbl 1460.62065

The location-dispersion regression model for heavy-tailed distributions is presented in more details. The associated inference methods are described after that: Estimation of the regression and dispersion functions, estimation of the conditional tail-index and extreme conditional quantiles. Asymptotic results are provided while the finite sample behavior of the estimators is illustrated on simulated data and on tsunami data. The next assumption is used that the response variable and the covariate are linked by a location-dispersion regression model \(Y = a(x) + b(x)Z\), where \(Z\) is a heavy-tailed random variable. This model is flexible since (i) no parametric assumptions are made on \(a(\cdot)\), \(b(\cdot)\) and \(Z\), (ii) it allows for heteroscedasticity via the function \(b(\cdot)\). Moreover, another feature of this model is that \(Y\) inherits its tail behavior from \(Z\) and thus does not depend on the covariate \(x\). Proofs are postponed to the Appendix.

MSC:

62G32 Statistics of extreme values; tail inference
62G30 Order statistics; empirical distribution functions
62G08 Nonparametric regression and quantile regression
62E20 Asymptotic distribution theory in statistics
60F10 Large deviations
62P12 Applications of statistics to environmental and related topics
86A15 Seismology (including tsunami modeling), earthquakes
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References:

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