Uniform Asymptotics for Nonparametric Quantile Regression with an Application to Testing Monotonicity

Understand

In this paper, we establish a uniform error rate of a Bahadur representation for local polynomial estimators of quantile regression functions.

• The error rate is uniform over a range of quantiles, a range of evaluation points in the regressors, and over a wide class of probabilities for observed random variables.
• Most of the existing results on Bahadur representations for local polynomial quantile regression estimators apply to the fixed data generating process.
• In the context of testing monotonicity where the null hypothesis is of a complex composite hypothesis, it is particularly relevant to establish Bahadur expansions that hold uniformly over a large class of data generating processes.