报告题目：高维线性模型的投影假设检验方法
报 告 人： 李长城 教授 大连理工大学
报告时间：2024年1月17日 10：00-11：00
报告地点：数学楼第一报告厅
校内联系人：韩月才 hanyc@jlu.edu.cn
报告摘要：In the talk, I will talk about two recent works with my collaborators. In the first work, we propose a new projection test for linear hypotheses on regression coefficient matrices in linear models with high-dimensional responses. We systematically study the theoretical properties of the proposed test. We derive the optimal projection matrix for any given projection dimension to achieve the best power and provide an upper bound for the optimal dimension of projection matrix. We further provide insights into how to construct the optimal projection matrix. One- and two-sample mean problems can be formulated as special cases of linear hypotheses studied in this article. We both theoretically and empirically demonstrate that the proposed test can outperform the existing ones for one- and two-sample mean problems. We conduct Monte Carlo simulation to examine the finite sample performance and illustrate the proposed test by a real data example. In the second work, we use the idea of projection test to derive a new method for testing the coefficient vector of the high-dimensional linear models, and establish the asymptotic normality of our proposed test statistic. We further derive the asymptotic relative efficiency (ARE) of the proposed test with respect to existing methods and also the optimality for the proposed test with signals of moderate sparsity.
报告人简介：李长城，大连理工大学数学科学学院教授。本科就读于北京大学数学科学学院，获得统计学学士学位；博士阶段师从美国宾夕法尼亚州州立大学统计系李润泽教授，进行高维统计领域的学习，获得统计学博士学位。研究兴趣主要包括高维统计推断及高维因果推断。在高维统计的理论、应用以及计算方面进行了一系列研究，文章发表于一流学术期刊Journal of American Statistical Association、Journal of Econometrics、Annals of Applied Statistics、Statistica Sinica等，入选国家级青年人才计划。
