Linear Hypothesis Testing in Linear Models with High Dimensional Responses

时间:2021-08-31         阅读:

光华讲坛——社会名流与企业家论坛第5857期

主题Linear Hypothesis Testing in Linear Models with High Dimensional Responses

主讲人宾州州立大学 李润泽教授

主持人统计学院 常晋源教授

时间2021年9月7日(周二)上午10:30-11:30

举办地点:腾讯会议,会议ID:423 739 370,会议密码:210907

主办单位:数据科学与商业智能联合实验室 统计学院 科研处

主讲人简介:

Runze Li is the Eberly Family Chair in Statistics, the Pennsyvlania State University. His research includes variable selection for high-dimensional data, feature screening for ultrahigh dimensional data, nonparametric and semiparametric regression modeling, and statistical applications to social behavioral science, neural science and engineering. He is a fellow of Institute of Mathematical Statistics, a fellow of American Statistical Association and a fellow of American Association for the Advancement of Science. He received various honors and awards including The United Nations' World Meteorological Organization Gerbier-Mumm International Award for 2012 and ICSA Distinguished Achievement Award in 2017. He served as editor of Annals of Statistics from 2013 to 2015.

李润泽教授是宾州州立大学Eberly Family统计学主席。他的研究领域包括高维数据的变量选择、超高维数据的特征筛选、非参数和半参数回归建模以及统计在社会行为科学、神经科学和工程中的应用。他是国际数理统计协会会士,美国统计学会会士和美国科学促进会会士。他获得有包括2012年联合国世界气象组织Gerbier-Mumm国际奖、2017年ICSA杰出成就奖在内的多项荣誉和奖项,是2013-2015年Annals of Statistics主编。

内容简介

In this paper, 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 first 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 paper. 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.

本文针对具有高维响应变量的线性模型回归系数矩阵的线性假设问题,提出了一种新的投影检验方法,并系统地研究了所提检验方法的理论性质。首先对于任意给定的投影维度,本文推导出了具有最佳功效的最优投影矩阵,并为投影矩阵的最优投影维度提供了上界。进一步,本文给出了最优投影矩阵的构建方法。单样本和两样本的均值检验问题都可以看作本文研究的线性假设问题的特例。从理论和数值研究上,本文均证明了所提检验方法优于现有针对单样本和两样本均值检验问题的检验方法。本文通过蒙特卡罗数值模拟研究了所提检验方法在有限样本下的表现情况,并通过实例研究证明了方法的有效性。

最新信息