Estimation of extreme conditional quantiles under a general tail-first-order condition
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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.
KeywordsExtreme quantile Local estimation Asymptotic normality
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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