應(yīng)yl7703永利官網(wǎng)趙學靖副教授邀請，美國康州紐海文大學（University of New Haven, CT, U.S.A.）梁家卷教授將于6月11日至6月12日訪問我校并作專題學術(shù)報告。

      報告題目：Using PCA for Multivariate Mean Testing in High Dimensional Data
      時      間：2018 年6月11日下午 4:30
      地      點：齊云樓911 報告廳
      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 The classical Wilks' Lambda-statistic is no longer applicable for the case of n≤p. In this paper, we propose the idea of applying principal component analysis (PCA) to dimension reduction for high-dimensional ANOVA.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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梁家卷教授簡介

      梁家卷教授分別于1987年在南開大學數(shù)學系獲碩士學位和1998年在香港浸會大學數(shù)學系獲博士學位。10/1998--8/2001于加州大學洛杉磯分校心理系和統(tǒng)計系從事博士后科研工作。 現(xiàn)為美國紐海文大學商學院市場營銷與數(shù)量分析系教授，主要研究興趣為統(tǒng)計學方法論及其在商業(yè)，經(jīng)濟和金融方面的應(yīng)用。Member of the American Statistical Association; Member of the International Chinese Statistical Association; Member of CAPA-CT。在國際學術(shù)刊物發(fā)表論文超過30篇，擔任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等期刊審稿人。關(guān)于梁家卷教授的更多信息，可參考 http://www.newhaven.edu/Faculty-Staff-Profiles/John-Liang/。