报告题目：Statistical inference for high-dimensional convoluted rank regression

报 告 人：郭旭教授

报告摘要：High-dimensional penalized rank regression is a powerful tool for modeling high-dimensional data due to its robustness and estimation efficiency. However, the non-smoothness of the rank loss brings great challenges to the computation. To solve this critical issue, high-dimensional convoluted rank regression has been recently proposed, introducing penalized convoluted rank regression estimators.  However, these developed estimators cannot be directly used to make inference. In this paper, we investigate the statistical inference problem of high-dimensional convoluted rank regression. The use of U-statistic in convoluted rank loss function brings challenges for the investigation. We begin by establishing estimation error bounds of penalized convoluted rank regression estimators under weaker conditions on the predictors. Building on this, we further introduce a debiased estimator and provide its Bahadur representation. Subsequently, a high-dimensional Gaussian approximation for the maximum deviation of the debiased estimator is derived, which allows us to construct simultaneous confidence intervals. For implementation, a  novel bootstrap procedure is proposed and its theoretical validity is also established. Finally, simulation and real data analysis are conducted to illustrate the merits of our proposed methods.

 报告人简介：郭旭博士，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。担任《应用概率统计》杂志第十届编委。现主持国家自然科学基金优秀青年基金。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。

报告时间：2024年6月23日9：30—11：00

报告地点：腾讯会议：876 452 953

联 系 人：王德辉