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# 兰州大学数学与统计学院学术报告——梁家卷教授

应兰州大学数学与统计学院赵学靖副教授邀请，美国康州纽海文大学（University of New Haven, CT, U.S.A.）梁家卷教授将于6月11日至6月12日访问兰州大学并作专题学术报告。

报告题目：Using PCA for Multivariate Mean Testing in High Dimensional Data

时   间：6月11日下午 4:30

地   点：齐云楼911 报告厅

Abstract：

The classical one-way analysis of variance (ANOVA) is a statistical method for comparing the mean differences between two or more groups of items when there is only one response variable. The ANOVA idea was extended to the simultaneous comparison between the mean responses from several populations with more than one response variable. This is called the multivariate analysis of variance (MANOVA). The existing method for MANOVA is based on the idea of maximum likelihood ratio (MLR) that results in the well-known Wilks' Lambda-statistic, which requires the sample size n must be greater than the dimension p (n>p). In modern medical research, however, the outcomes from a large number of response variables can be easily measured from experiments with the help of modern medical instruments, while the number of patients could be limited due to experimental complexity or high cost. This results in the case that the sample size may be smaller than the dimension (n≤p). The classical Wilks' Lambda-statistic is no longer applicable for the case of n≤p. In this paper, we propose the idea of applying principal component analysis (PCA) to dimension reduction for high-dimensional ANOVA. The new method is applicable for any sample size and dimension. Based on the theory of spherical distributions, the exact null distribution of the test statistics are proved to follow the F-distribution.  Monte Carlo simulation results show that the dimension reduction approach to high-dimensional ANOVA has competitive power performance. It dominates over the classical Wilks' Lambda-statistic significantly when n>p with n being close to p. An application of the new MANOVA method is illustrated by real medical datasets.

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梁家卷教授分别于1987年在南开大学数学系获硕士学位和1998年在香港浸会大学数学系获博士学位。10/1998--8/2001于加州大学洛杉矶分校心理系和统计系从事博士后科研工作。 现为美国纽海文大学商学院市场营销与数量分析系教授，主要研究兴趣为统计学方法论及其在商业，经济和金融方面的应用。Member of the American Statistical Association; Member of the International Chinese Statistical Association; Member of CAPA-CT。在国际学术刊物发表论文超过30篇，担任Journal of the Royal Statistical Society (Series B and C)、Metrika, Computational Statistics & Data Analysis, Communications in Statistics –Theory and Method, TEST, Journal of Multivariate Analysis, Journal of Statistical Planning & Inference, Statistics in Medicine, Statistics, Statistics and Probability Letters等期刊审稿人。关于梁家卷教授的更多信息，可参考 http://www.newhaven.edu/Faculty-Staff-Profiles/John-Liang/

数学与统计学院
萃英学院
2018年6月7日

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