A Simple Nonparametric Approach for Estimation and Inference of Conditional Quantile Functions

Abstract

In this paper we present a new nonparametric method for estimating a conditional quantile function and develop its weak convergence theory. The proposed estimator is computationally easy-to-implement, and automatically ensures quantile monotonicity by construction. For inference, we propose to use a residual bootstrap method. The Monte Carlo simulations show that our new estimator compares well with the checkfunction-based estimator in terms of estimation mean squared error (MSE), and the bootstrap confidence bands give adequate coverage probabilities. An empirical example considering a dataset from Canadian high school graduate earnings illustrates that the proposed method delivers a more reasonable quantile estimate than the check-function counterpart.