Confidence Corridors for Multivariate Generalized Quantile Regression

TL;DR

This paper develops confidence corridors for multivariate generalized quantile regression functions using advanced asymptotic theory and bootstrap methods, improving coverage accuracy especially for small samples.

Contribution

It introduces a novel approach combining asymptotic results and bootstrap procedures for constructing confidence corridors in multivariate nonparametric quantile regression.

Findings

Bootstrap confidence corridors outperform asymptotic bands in coverage accuracy

Finite sample properties are validated through simulation studies

Application to a real employment program demonstrates practical utility

Abstract

We focus on the construction of confidence corridors for multivariate nonparametric generalized quantile regression functions. This construction is based on asymptotic results for the maximal deviation between a suitable nonparametric estimator and the true function of interest which follow after a series of approximation steps including a Bahadur representation, a new strong approximation theorem and exponential tail inequalities for Gaussian random fields. As a byproduct we also obtain confidence corridors for the regression function in the classical mean regression. In order to deal with the problem of slowly decreasing error in coverage probability of the asymptotic confidence corridors, which results in meager coverage for small sample sizes, a simple bootstrap procedure is designed based on the leading term of the Bahadur representation. The finite sample properties of both procedures are investigated by means of a simulation study and it is demonstrated that the bootstrap procedure considerably outperforms the asymptotic bands in terms of coverage accuracy. Finally, the bootstrap confidence corridors are used to study the efficacy of the National Supported Work Demonstration, which is a randomized employment enhancement program launched in the 1970s. This article has supplementary materials.