Multivariate Analysis -104 Academic Year
多變量分析 -104 學年度
本課程是由 國立陽明交通大學統計學研究所提供。
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.
課程用書：
Johnson, R.A. and Wichern, D.W., 2007. Applied Multivariate Statistical Analysis (6th Edition). Prentice Hall, Upper Saddle River, NJ.
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| 授課教師 | 統計學研究所 黃冠華老師 |
|---|---|
| 課程學分 | 3學分 |
| 授課年度 | 104學年度 |
| 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 |
| 課程提供 | 課程影音 課程綱要 課程行事曆 |
| 週次 | 課程內容 | 課程影音 | 課程下載 |
|---|---|---|---|
| 第一週 | Introduction | 線上觀看 | MP4下載 |
| 第一週 | Aspects of multivariate analysis -introduction -review of linear algebra and matrices | 線上觀看 | MP4下載 |
| 第一週 | Aspects of multivariate analysis -introduction -review of linear algebra and matrices | 線上觀看 | MP4下載 |
| 第二週 | Multivariate normal distribution -density and properties -sampling from multivariate normal and MLE -sampling distribution and large sample behavior of X and S -assessing the assumption of normality -transformation to near normality | 線上觀看 | MP4下載 |
| 第三週 | Multivariate normal distribution -density and properties -sampling from multivariate normal and MLE -sampling distribution and large sample behavior of X and S -assessing the assumption of normality -transformation to near normality | 線上觀看 | MP4下載 |
| 第四週 | Comparisons of several multivariate means -paired comparisons and repeated measures design -comparing mean vectors from two populations -comparing several multivariate population means (one-way MANOVA) | 線上觀看 | MP4下載 |
| 第五週 | Principal components -introduction -population principal components -summarizing sample variation by principal components -large sample inferences | 線上觀看 | MP4下載 |
| 第六週 | Factor analysis (1/2) -introduction -orthogonal factor model -methods of estimation | 線上觀看 | MP4下載 |
| 第八週 | Factor analysis (2/2) -factor rotation -factor scores | 線上觀看 | MP4下載 |
| 第十週 | Clustering (1/2) -introduction -similarity measures -hierarchical clustering methods | 線上觀看 | MP4下載 |
| 第十一週 | Clustering (2/2) -k-means clustering methods -model-based clustering -multidimensional scaling | 線上觀看 | MP4下載 |
| 第十二週 | Discrimination and classification (1/2) -introduction | 線上觀看 | MP4下載 |
| 第十三週 | Discrimination and classification (2/2) -evaluation of classification functions -classification with several populations -fisher's method for discriminating among several populations | 線上觀看 | MP4下載 |
| 第十四週 | Canonical correlation analysis (1/2) -introduction -canonical variates and canonical correlations -interpreting the population canonical variables | 線上觀看 | MP4下載 |
| 第十五週 | Canonical correlation analysis (2/2) -sample canonical variates and sample canonical correlations -sample descriptive measures of goodness-of-fit -proportions of explained sample variance -large sample inferences | 線上觀看 | MP4下載 |
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.
本課程行事曆提供課程進度與考試資訊。
週次 | 上課日期 | 課程進度、內容、主題 |
| 1 | 2/23 | Aspects of multivariate analysis -introduction -review of linear algebra and matrices Matrix algebra and random vectors -random vectors -distance -sample geometry -random sampling of sample mean vector and covariance matrix -generalized variance -matrix operations of sample values |
| 2 | 3/01 | Multivariate normal distribution -density and properties -sampling from multivariate normal and MLE -sampling distribution and large sample behavior of X and S -assessing the assumption of normality -transformation to near normality |
| 3 | 3/08 | Inferences about a mean vector -inference for a normal population mean -Hotelling's T2 and likelihood ratio test -confidence regions and simultaneous comparisons of component means -large sample inferences about a population mean vector |
| 4 | 3/15 | Comparisons of several multivariate means -paired comparisons and repeated measures design -comparing mean vectors from two populations -comparing several multivariate population means (one-way MANOVA) |
| 5 | 3/22 | Principal components -introduction -population principal components -summarizing sample variation by principal components -large sample inferences |
| 6 | 3/29 | Factor analysis (1/2) -introduction -orthogonal factor model -methods of estimation |
| 7 | 4/05 | Day-off |
| 8 | 4/12 | Factor analysis (2/2) -factor rotation -factor scores |
| 9 | 4/19 | Midterm exam |
| 10 | 4/26 | Clustering (1/2) -introduction -similarity measures -hierarchical clustering methods |
| 11 | 05/03 | Clustering (2/2) -k-means clustering methods -model-based clustering -multidimensional scaling |
| 12 | 05/10 | Discrimination and classification (1/2) -introduction |
| 13 | 05/17 | Discrimination and classification (2/2) -evaluation of classification functions -classification with several populations -fisher's method for discriminating among several populations |
| 14 | 05/24 | Canonical correlation analysis (1/2) -introduction -canonical variates and canonical correlations -interpreting the population canonical variables |
| 15 | 05/31 | Canonical correlation analysis (2/2) -sample canonical variates and sample canonical correlations -sample descriptive measures of goodness-of-fit -proportions of explained sample variance -large sample inferences |
| 16 | 6/07 | Day-off |
| 17 | 6/14 | Final exam |
課程專區
選單