Nonparametric conditional quantile estimation: A locally weighted quantile kernel approach

Nonparametric conditional cumulative distribution function (CDF) estimation has emerged as a powerful tool having widespread potential application, which has led to a literature on estimators of conditional quantile functions that are obtained via inversion of the nonparametrically estimated conditional CDF. Other nonparametric estimators of conditional quantiles that are based on an alternative characterization of the quantile (i.e., as the function that minimizes the expectation of the check-function) have also appeared in the literature. In this paper, we propose a novel nonparametric approach. Relative to its inverse-CDF-based and the check-function-based peers, our proposed estimator has a simple expression. We also show that under certain conditions, our estimator is more efficient in tail regions when the data has unbounded support (our theoretical results underscore this property). Theoretical underpinnings are developed, a method for data-driven smoothing parameter selection is provided, and Monte Carlo simulations and empirical examples are considered. Two empirical examples illustrate how the proposed approach can deliver more reasonable quantile and quantile derivative estimates than its inverse-CDF-based and the check-function-based counterparts, particularly in tail regions.