Abstract
We consider the estimation of an extreme conditional quantile. In a first part, we propose a new tail condition in order to establish the asymptotic distribution of an extreme conditional quantile estimator. Next, a general class of estimators is introduced, which encompasses, among others, kernel or nearest neighbors types of estimators. A unified theorem of the asymptotic normality for this general class of estimators is provided under the new tail condition and illustrated on the different well-known examples. A comparison between different estimators belonging to this class is provided on a small simulation study and illustrated on a real dataset on earthquake magnitudes.
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The authors would like to thank the reviewers, the associate editor and editor for their helpful comments and suggestions that led to substantial improvement of the paper.
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Gardes, L., Guillou, A. & Roman, C. Estimation of extreme conditional quantiles under a general tail-first-order condition. Ann Inst Stat Math 72, 915–943 (2020). https://doi.org/10.1007/s10463-019-00713-7
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DOI: https://doi.org/10.1007/s10463-019-00713-7