Speaker: Prof. Xu Guo(Beijing Normal University)
Time: 2025-04-07 14:30-16:00
Venue: Lecture Hall 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.
Guo Xu is currently a Professor and Doctoral Advisor at the School of Statistics, Beijing Normal University. His research focuses on theoretical methodologies and applications of complex hypothesis testing in regression analysis, with recent emphasis on developing appropriate and effective testing methods for high-dimensional data. Some of his work has been published in top-tier journals such as JRSSB, JASA, Biometrika, and JOE.
He is currently the principal investigator of a National Natural Science Foundation of China (NSFC) Young Scientists Fund (Category B, formerly the Excellent Young Scientists Fund). His teaching excellence has been recognized with multiple awards, including: BNU’s 11th "Top 10 Most Popular Teachers Among Undergraduates", First Prize in BNU’s 18th Young Faculty Teaching Competition, Third Prize in Beijing’s 13th Young Faculty Teaching Competition.
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