EXTREME QUANTILE ESTIMATION BASED ON THE TAIL SINGLE-INDEX MODEL

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 ???n-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.