Nonextreme regression quantiles are estimated nonparametrically on the basis of local polynomial approximations to the true conditional quantile function. The consistency of the estimator is shown. The asymptotic normality is proven and the asymptotic confidence interval for the regression...

We discuss the estimation of the tail index of a heavy-tailed distribution when covariate information is available. The approach followed here is based on the technique of local polynomial maximum likelihood estimation. The generalized Pareto distribution is fitted locally to exceedances over a...