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梁家卷:Generalization of Classical Mean Test and ItsApplications(古典均值检验的推广及其应用)

日期:2019-05-21      来源:统计学院 科技处    [字体: ]

题 目:Generalizationof Classical Mean Test and Its Applications(古典均值检验的推广及其应用)

主讲人:梁家卷教授

时 间:2019年5月22日(星期三)10:30--12:30

地 点:段家滩校区MBA小案例教室

内容摘要:The classicalmean test is the most common parametric statistical inference with theunderlying assumption of normal distribution on the sample data. The popularmethod for this purpose is the Student’s t-test. When the normal assumption isnot satisfied, the t-test is theoretically no longer applicable. It iswell-known that the traditional t-test can be generalized to two-sample meancomparison, and the problem of two-sample mean comparison can be generalized tothe problem of multiple mean comparison –one way analysis of variance (ANOVA).In the multivariate case, the single-sample mean test is replaced with theHotelling’s T2-test, and the two-sample mean comparison and the case ofmultiple mean comparison become multivariate analysis of variance (MANOVA). Thepopular method for MANOVA is the Wilks Lambda-test. All of these classicalmethods are based on the normal assumption. In the univariate case, multiplemean comparison requires equal variance assumption; in the multivariate case,multiple mean comparison requires both equal covariance assumption and that thetotal sample size must be greater than the dimension of the multivariateobservations. In this talk, I will introduce the basic theory of sphericaldistribution and the spherical matrix distribution, and apply the theory toconstruction of new tests for mean comparison that may violate the normalassumption, or may not have equal variances across the multiplepopulations,or the total sample sizemust be smaller than the dimension of the multivariate observations. Someexamples are given to illustrate the wide applications of the new tests.

报告人简介:梁家卷毕业于南开大学数学系并取得数学本科(1984)和多元统计硕士(1987),取得中国科学院应用数学研究所应用数学博士(1998)和香港浸会大学数学系数理统计博士(1998)。梁家卷博士于1998至2001年在美国加州大学洛杉矶分校统计系和心理系作博士后研究并于2001年9月至今在美国康州纽海文大学任教,教授。个人研究成果包括超过二十篇SCI刊物专业学术论文和十多篇论文集的贡献文章及专业文章。

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