報告題目：高維線性模型的投影假設檢驗方法
報 告 人： 李長城 教授 大連理工大學
報告時間：2024年1月17日 10：00-11：00
報告地點：數學樓第一報告廳
校内聯系人：韓月才 hanyc@jlu.edu.cn
報告摘要：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.
報告人簡介：李長城，大連理工大學數學科學學院教授。本科就讀于北京大學數學科學學院，獲得統計學學士學位；博士階段師從美國賓夕法尼亞州州立大學統計系李潤澤教授，進行高維統計領域的學習，獲得統計學博士學位。研究興趣主要包括高維統計推斷及高維因果推斷。在高維統計的理論、應用以及計算方面進行了一系列研究，文章發表于一流學術期刊Journal of American Statistical Association、Journal of Econometrics、Annals of Applied Statistics、Statistica Sinica等，入選國家級青年人才計劃。
