NATIONAL CHIAO TUNG UNIVERSITY

INSTITUTE OF STATISTICS

MULTIVARIATE ANALYSIS

SPRING 2018

Instructor:	Guan-Hua Huang, Ph.D.
	Office: 423 Joint Education Hall
	Phone: 03-513-1334
	Email: ghuang@stat.nctu.edu.tw
Class meetings:	Monday 9:00-12:00 at A203 Joint Education Hall
Office hours:	By appointment
Class website:	http://ghuang.stat.nctu.edu.tw/course/multivariate18/
Credit:	Three (3) credits

COURSE SUMMARY

The aims of this course are

Ÿ To illustrate extensions of univariate statistical methodology to multivariate data.

Ÿ To introduce students to some of the distinctive statistical methodologies which arise only in multivariate data.

Ÿ 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, canonical correlation analysis, cluster analysis, discrimination and classification, machine learning.

The course uses the R software for statistical computing. Students are expected to be familiar with the usage of the software.

HANDOUTS AND TEXTBOOKS

Handouts corresponding to each lecture will be available on the class website before each class. The required textbook for this course is:

Johnson, R.A. and Wichern, D.W., 2007. Applied Multivariate Statistical Analysis (6th Edition). Prentice Hall, Upper Saddle River, NJ.

Reading assignments will be made primary in this book.

PREREQUISITES

Students are expected to have background on undergraduate linear algebra, probability, mathematical statistics, and linear regression. Computer programming knowledge on R and/or C/C++ is required.

METHOD OF STUDENT EVALUATION

The course grade will be based on 5 homework assignments (50%), 1 midterm exam (20%), and 1 final exam (30%).

COURSE OUTLINE

Readings refer to: Johnson, R.A. and Wichern, D.W., 2007. Applied Multivariate Statistical Analysis (6th Edition). (AMSA)

Module	Topic	Reading (pages)
1	Aspects of multivariate analysis: - introduction - review of linear algebra and matrices	1-30, 49-110
2	Random vectors and random sampling: - random vectors/matrices - distance - the sample - random sampling of the sample mean vector and covariance matrix - generalized variance - matrix operations of sample values	30-37, 60-78, 111-148
3	Multivariate normal distribution: - density and properties - sampling from multivariate normal and MLE - sampling distribution and large sample behavior of and S - assessing the assumption of normality - transformation to near normality	149-200
4	Inferences about a mean vector: - inference for a normal population mean - Hotelling's T^2 and likelihood ratio test - confidence regions and simultaneous comparisons of component means - large sample inferences about a population mean vector	210-238
5	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)	273-312
6	Principal components: - introduction - population principal components - summarizing sample variation by principal components - large sample inferences	430-459
7	Factor analysis: - introduction - orthogonal factor model - methods of estimation - factor rotation - factor scores	481-526
8	Canonical correlation analysis: - introduction - population and sample canonical variates and canonical correlations - sample descriptive measures of goodness	539-563
9	Clustering: - introduction - similarity measures - hierarchical clustering methods - k-means clustering methods - multidimensional scaling	671-715
10	Discrimination and classification: - introduction - separation and classification for two populations - classification with two multivariate normal populations - evaluating classification functions - fisher discriminant function - classification with several population	575-644
11	Machine learning - support vector machine - neural networks - classification and regression tree