Weighted Average Estimator in Nonparametric Quantile Regression for the Data of Higher Dimensions

The standard approach to the asymptotic analysis of nonparametric quantile regression is the use of the Bahadur expansion. However, it restricts the possible dimensionality of the covariate vector, given the optimal choice of bandwidth. We propose the alternative weighted average estimator for nonparametric quantile regression models, which allows to obtain inference results for the covariates of higher dimensions in nonparametric setting. The paper exploits alternative mathematical approach: we apply the higher order Edgeworth expansions to calculate the moments of Bahadur expansions of the nonparametric estimators. The proposed estimator can be further applied for the testing procedures and in some treatment settings, as well as in single-index and partially-linear models. We conduct a series of simulations that confirm our findings.