报告摘要：

In practice, measurement error data is frequently encountered and needs to behandled appropriately. As a result of additional bias induced by measurement error,many existing estimation methods fail to achieve satisfactory performances. This paperstudies high-dimensional partially linear measurement error models. It proposesa calibrated equilibrium (CARE) estimation method, calibrating the bias caused bymeasurement error and overcoming the technical difficulty of the objective functionunbounded from below in high-dimensional cases due to non-convexity. To facilitatethe applications of CARE estimation method, a bootstrap approach for approximatingcovariance matrix of measurement errors is introduced. For the high dimensionalor ultra-high dimensional partially linear measurement error models, a calibratedequilibrium multiple double selection (CARE–MUSE) algorithm, a novel multipletesting method, is suggested to control the false discovery rate (FDR) of significantcovariates. We obtain the oracle inequalities for prediction risk and estimation errorand the bound of the number of falsely discovered signs for the CARE estimatorunder some regularity conditions. The convergence rate of the estimator of the nonparametricfunction is also established. FDR and power guarantee for CARE–MUSEalgorithm are investigated under a weaker minimum signal condition, which is insufficientfor the CARE estimator to achieve sign consistency. Extensive simulationstudies and an actual data application demonstrate the satisfactory finite sampleperformance of the proposed methods.

报告人简介：

李高荣，北京师范大学统计学院教授，博士生导师，北京师范大学第十二届“最受本科生欢迎的十佳教师”。主要研究方向是非参数统计、高维统计、统计学习、纵向数据、测量误差数据和因果推断等。迄今为止，在Annals of Statistics, Journal of the American Statistical Association, Journal of Business & Economic Statistics, Statistics and Computing, 《中国科学：数学》和《统计研究》等学术期刊上发表学术论文120余篇。出版4部著作：《纵向数据半参数模型》、《现代测量误差模型》(入选“现代数学基础丛书”系列)、《多元统计分析》(入选“统计与数据科学丛书”系列，2023年荣获北京高校优质本科教材）和统计学习（R语言版）。主持国家自然科学基金、北京市自然科学基金和北京市教委科技计划面上项目等国家和省部级科研项目10多项。