Nonparametric estimation of conditional quantile functions in the presence of irrelevant covariates

Allowing for the existence of irrelevant covariates, we study the problem of estimating a conditional quantile function nonparametrically with mixed discrete and continuous data. We estimate the conditional quantile regression function using the check-function-based kernel method and suggest a data-driven cross-validation (CV) approach to simultaneously determine the optimal smoothing parameters and remove the irrelevant covariates. When the number of covariates is large, we first use a screening method to remove the irrelevant covariates and then apply the CV criterion to those that survive the screening procedure. Simulations and an empirical application demonstrate the usefulness of the proposed methods.