Abstract：This paper aims to develop new estimation and inference procedures for high-dimensional partially linear quantile regression (QR) models. Compared with least squares methods, QR presents unique challenges due to the non-smoothness of its loss function and the non-additivity of conditional quantile. To address the challenges, we apply convolution-smoothing technique to handle the non-smoothness and weighted projection technique to deal with the non-additivity. Specifically, the estimation procedure approximates the non-parametric function by B-spline and employs an L1 regularization for linear coefficients. Theoretically, we establish a new non-asymptotic smoothness-adjusted second-order effect property which holds for a wide range of non-parametric regression methods. Furthermore, we propose a debiased Lasso estimator using a newly proposed projection strategy. The strategy involves estimating the conditional density function of random errors, which introduces an uncontrollable error. We adopt the double smoothing technique to address the issue and establish asymptotic normality for debiased estimator. The proposed methods are evaluated through numerical simulations and an analysis of the relationship between maternal age and infant birth weight.
郭旭，现为北京师范大学统计学院教授，博士生导师。郭老师一直从事回归分析中复杂假设检验的理论方法及应用研究，近年来旨在对高维数据发展适当有效的检验方法。部分成果发表在JRSSB，JASA，Biometrika和JOE。现主持国家自然科学基金青年科学基金项目B类（原优秀青年科学基金）。曾荣获北师大第十一届“最受本科生欢迎的十佳教师”，北师大第十八届青教赛一等奖和北京市第十三届青教赛三等奖。
