报告题目：高维部分线性分位数回归模型的估计和推断

报告时间：2025-04-07  14:30-16:00

报 告 人：郭旭  教授（北京师范大学）

报告地点：雷军科技楼六楼报告厅（601）

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.