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This paper studies the estimation of extreme conditional quantile for single-index varying-coefficient models (SIVCM). Our contribution is a three-step extreme quantile regression procedure for SIVCM. In the first step, we estimate the intermediate conditional quantile in a quantile regression framework. In the second step, we estimate the extreme value index (EVI) based on the estimated intermediate quantile. In the third step, we extrapolate the intermediate conditional quantile to the extreme tails by adapting the extreme value theory (EVT). We obtain the asymptotation of tail single-index varying-coefficient estimators and demonstrate through simulation study and real data example that the proposed methods enjoy higher accuracy than the conventional quantile regression estimates.

Extreme quantile regression for tail single-index varying-coefficient models