Nonparametric Estimation of Extreme Conditional Quantiles with Functional Covariate
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Estimation of the extreme conditional quantiles with functional covariate is an important problem in quantile regression. The existing methods, however, are only applicable for heavy-tailed distributions with a positive conditional tail index. In this paper, we propose a new framework for estimating the extreme conditional quantiles with functional covariate that combines the nonparametric modeling techniques and extreme value theory systematically. Our proposed method is widely applicable, no matter whether the conditional distribution of a response variable Y given a vector of functional covariates X is short, light or heavy-tailed. It thus enriches the existing literature.
KeywordsExtreme conditional quantile extreme value theory nonparametric modeling functional covariate
MR(2010) Subject Classification62G32
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The authors thank the editor, the associate editor and two referees for their constructive comments that have led to a substantial improvement of the paper.