Nonparametric Estimation of Extreme Conditional Quantiles

The estimation of extreme conditional quantiles is an important issue in different scientific disciplines. Up to now, the extreme value literature focused mainly on estimation procedures based on i.i.d. samples. On the other hand, quantile regression based procedures work well for estimation within the data range i.e. the estimation of nonextreme quantiles but break down when main interest is in extrapolation. Our contribution is a two-step procedure for estimating extreme conditional quantiles. In a first step nonextreme conditional quantiles are estimated nonparametrically using a local version of the Koenker and Bassett (1978) regression quantile methodology. Next, these nonparametric quantile estimates are used as analogues of univariate order statistics in well known extreme quantile estimators. The performance of the method is evaluated for both heavy tailed distributions and distributions with a finite right endpoint using a small sample simulation study. A bootstrap procedure is developed to guide in the selection of an optimal local bandwidth. Finally the procedure is illustrated in three cases.