No-Crossing Single-Index Quantile Regression Curve Estimation
针对单指标分位数回归中估计曲线可能交叉的问题，提出保证无交叉的估计方法，并扩展到复合分位数回归，通过模拟和实际数据验证了方法的有效性。
Copyright © 2022 The Authors. Single-index quantile regression (QR) models can avoid the curse of dimensionality in nonparametric problems by assuming that the response is only related to a single linear combination of the covariates. Like the standard parametric or nonparametric QR whose estimated curves may cross, the single-index QR can also suffer quantile crossing, leading to an invalid distribution for the response. This issue has attracted considerable attention in the literature in the recent year. In this article, we consider single-index models, develop methods for QR that guarantee noncrossing quantile curves, and extend the methods and results to composite quantile regression. The asymptotic properties of the proposed estimators are derived and their advantages over existing methods are explained. Simulation studies and a real data application are conducted to illustrate the finite sample performance of the proposed methods.