Symmetrized Nearest Neighbor Kernel Estimator of the Conditional Quantiles

Abstract

Stute (1986) has introduced the symmetrized nearest neighbor (SNN) kernel estimator to estimate the conditional quantiles in the univariate case. This estimator is here extended to the multivariate case. Two methods were proposed for the derivation of the asymptotic normality of the proposed estimators. The first method considers two different quantiles estimated at the same conditional point. In the other one, the conditional quantile estimated at  different conditional points is considered. The construction of the confidence bands as well as the problem of bandwidth selection to avoid the boundary effects were discussed. Empirical studies are performed to assess the performance of the SNN kernel estimator in finite samples. Simulation results attested a reasonably good performance of the proposed estimator.