Multivariate Analysis -104 Academic Year
This course is provided by the NYCU Institute of Statistic .
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.
Textbooks：
Johnson, R.A. and Wichern, D.W., 2007. Applied Multivariate Statistical Analysis (6th Edition). Prentice Hall, Upper Saddle River, NJ.
For perfect learning results, please buy textbooks!
| Instructor(s) | Institute of Statistic Prof. Guan-Hua Huang |
|---|---|
| Course Credits | 3 Credits |
| Academic Year | 104 Academic Year |
| Level | Graduate Student |
| Prior Knowledge | Linear Algebra, Probability, Mathematical Statistics and Linear Regression |
| Related Resources | Course Video Course Syllabus Course Calendar |
| Week | Course Content | Course Video | Course Download |
|---|---|---|---|
| Week 1 | Introduction | Watch Online | MP4 Download |
| Week 1 | Aspects of multivariate analysis -introduction -review of linear algebra and matrices | Watch Online | MP4 Download |
| Week 1 | 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 | Watch Online | MP4 Download |
| Week 2 | 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 | Watch Online | MP4 Download |
| Week 3 | 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 | Watch Online | MP4 Download |
| Week 4 | 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) | Watch Online | MP4 Download |
| Week 5 | Principal components -introduction -population principal components -summarizing sample variation by principal components -large sample inferences | Watch Online | MP4 Download |
| Week 6 | Factor analysis (1/2) -introduction -orthogonal factor model -methods of estimation | Watch Online | MP4 Download |
| Week 8 | Factor analysis (2/2) -factor rotation -factor scores | Watch Online | MP4 Download |
| Week 10 | Clustering (1/2) -introduction -similarity measures -hierarchical clustering methods | Watch Online | MP4 Download |
| Week 11 | Clustering (2/2) -k-means clustering methods -model-based clustering -multidimensional scaling | Watch Online | MP4 Download |
| Week 12 | Discrimination and classification (1/2) -introduction | Watch Online | MP4 Download |
| Week 13 | Discrimination and classification (2/2) -evaluation of classification functions -classification with several populations -fisher's method for discriminating among several populations | Watch Online | MP4 Download |
| Week 14 | Canonical correlation analysis (1/2) -introduction -canonical variates and canonical correlations -interpreting the population canonical variables | Watch Online | MP4 Download |
| Week 15 | 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 | Watch Online | MP4 Download |
Course Objectives
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.
Course Outline
| Unit | Content | Textbook Scope |
| 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 |
Reference Books
Johnson, R.A. and Wichern, D.W., 2007. Applied Multivariate Statistical Analysis (6th Edition). Prentice Hall, Upper Saddle River, NJ.
This course calendar provides information on course progress and exams.
| Unit | Date | Course Progress, Contents, Topics |
| 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 |
COURSE
Menu