Tail dimension reduction for extreme quantile estimation
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In a regression context where a response variable Y ∈ ℝ is recorded with a covariate X ∈ ℝ p , two situations can occur simultaneously: (a) we are interested in the tail of the conditional distribution and not on the central part of the distribution and (b) the number p of regressors is large. To our knowledge, these two situations have only been considered separately in the literature. The aim of this paper is to propose a new dimension reduction approach adapted to the tail of the distribution in order to propose an efficient conditional extreme quantile estimator when the dimension p is large. The results are illustrated on simulated data and on a real dataset.
KeywordsRegression Extreme quantile Dimension reduction Kernel smoothing
AMS 2000 Subject Classifications62G32 62G08 62G05 62G20
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- de Haan, L., Ferreira, A.: Extreme Value Theory: An Introduction. Springer (2006)Google Scholar
- Fraga Alves, M.I., Gomes, M.I., de Haan, L., Neves, C.: A note on second order conditions in extreme value theory: linking general and heavy tail conditions. REVSTAT - Stat. J. 5(3), 285–304 (2007)Google Scholar
- Han, S., Bian, H., Feng, Y., Liu, A., Li, Zeng, F., Zhang, X: Analysis of the relationship between O3,, NO and NO2 in Tianjin, China. Aerosol Air Qual. Res. 11, 128–139 (2011)Google Scholar