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Statistica Sinica 32 (2022), 893-914

EXTREME QUANTILE ESTIMATION BASED
ON THE TAIL SINGLE-INDEX MODEL

Wen Xu1 , Huixia Judy Wang2 and Deyuan Li1

1Fudan University and 2The George Washington University

Abstract: It is important to quantify and predict rare events that have significant societal effects. Existing works on analyzing such events rely mainly on either inflexible parametric models or nonparametric models that are subject to "the curse of dimensionality". We propose a new semiparametric approach based on the tail single-index model to obtain a better balance between model flexibility and parsimony. The procedure involves three steps. First, we obtain a vn-estimator of the index parameter. Next, we apply the local polynomial regression to estimate the intermediate conditional quantiles. Lastly, these quantiles are extrapolated to the tails to estimate the extreme conditional quantiles. We establish the asymptotic properties of the proposed estimators. Furthermore, we demonstrate using a simulation and an analysis of Los Angeles mortality and air pollution data that the proposed method is easy to compute and leads to more stable and accurate estimations than those of alternative methods..

Key words and phrases: Extreme quantile, local linear regression, semi-parametric, single-index, tail.

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