標題: 多變量分析Multivariate Analysis 作者: 黃冠華Open Education Office開放教育推動中心 公開日期: 2015 摘要: 課程首頁 The aims of this course are: (1) To illustrate extensions of univariate statistical methodology to multivariate data. (2) To introduce students to some of the distinctive statistical methodologies which arise only in multivariate data. (3) To introduce students to some of the computational techniques required for multivariate analysis available in standard statistical packages. Topics include: multivariate techniques and analyses, multivariate analysis of variance, principal component analysis and factor analysis, cluster analysis, discrimination and classification.課程概述與目標 The aims of this course are: (1) To illustrate extensions of univariate statistical methodology to multivariate data. (2) To introduce students to some of the distinctive statistical methodologies which arise only in multivariate data. (3) To introduce students to some of the computational techniques required for multivariate analysis available in standard statistical packages. Topics include: multivariate techniques and analyses, multivariate analysis of variance, principal component analysis and factor analysis, cluster analysis, discrimination and classification.   課程大綱 單元主題 內容綱要 課本範圍(頁數) Aspects of multivariate analysis　 (1) introduction (2) review of linear algebra and matrices 1-30, 49-110 Matrix algebra and random vectors (1) random vectors (2) distance (3) sample geometry (4) random sampling of sample mean vector and covariance matrix (5) generalized variance (6) matrix operations of sample values 30-37, 60-78, 111-148 Multivariate normal distribution (1) density and properties (2) sampling from multivariate normal and MLE (3) sampling distribution and large sample behavior of X and S (4) assessing the assumption of normality (5) transformation to near normality 149-209 Inferences about a mean vector (1) inference for a normal population mean (2) Hotelling's T2 and likelihood ratio test (3) confidence regions and simultaneous comparisons of component means (4) large sample inferences about a population mean vector 210-238 Comparisons of several multivariate means (1) paired comparisons and repeated measures design (2) comparing mean vectors from two populations (3) comparing several multivariate population means (one-way MANOVA) 273-312 Principal components (1) introduction (2) population principal components (3) summarizing sample variation by principal components (4) large sample inferences 430-459 Factor analysis (1) introduction (2) orthogonal factor model (3) methods of estimation (4) factor rotation (5) factor scores 481-526 Clustering (1) introduction (2) similarity measures (3) hierarchical clustering methods (4) k-means clustering methods (5) multidimensional scaling 671-715 Discrimination and classification (1) introduction (2) separation and classification for two populations (3) classification with two multivariate normal populations (4) evaluating classification functions (5) fisher discriminant function (6) classification with several population 575-644   參考用書 Johnson, R.A. and Wichern, D.W., 2007. Applied Multivariate Statistical Analysis (6th Edition). Prentice Hall, Upper Saddle River, NJ.   評分標準 項目 百分比 4 homework assignments 50% Midterm exam 20% Final exam 30%    授課對象：碩士生預備知識：線性代數、機率、數學統計與線性迴歸 URI: http://ocw.nctu.edu.tw/course_detail.php?bgid=1&nid=543http://hdl.handle.net/11536/132461 Appears in Collections: Open Course Ware