MULTIVARIATE ANALYSIS
FALL 2008
Instructor: 
GuanHua Huang, Ph.D. 

Office: 423 Joint Education Hall 

Phone: 035131334 

Email: ghuang@stat.nctu.edu.tw 
Class meetings: 
Wednesday 9:0012:00 at 406 Joint Education Hall 
Office hours: 
By appointment 
Class website: 
http://www.stat.nctu.edu.tw/subhtml/source/teachers/ghuang/course/multivariate08/ 
Credit: 
Three (3) credits 
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, cluster analysis, discrimination and
classification, structural equation models.
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,
Reading
assignments will be made primary
in this book.
Students are expected to have
background on undergraduate linear algebra, probability, mathematical
statistics, and linear regression.
The course grade will be based on three homework assignments (50%), one midterm exam (20%), and one final exam (30%).
COURSE OUTLINE
Module 
Topic 

1 
Aspects of multivariate analysis:  introduction  review of linear algebra and matrices 
130, 49110 
2 
Random vectors and random sampling:  random vectors  distance  sample geometry  random sampling of sample mean vector and covariance matrix  generalized variance  matrix operations of sample values 
3037, 6678, 111148 
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 
149209 
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 
210238 
5 
Comparisons of several multivariate means:  paired comparisons and repeated measures design  comparing mean vectors from two populations  comparing several multivariate population means (oneway MANOVA) 
273312 
6 
Principal components:  introduction  population principal components  summarizing sample variation by principal components  large sample inferences 
430459 
7 
Factor analysis:  introduction  orthogonal factor model  methods of estimation  factor rotation  factor scores 
481526 
8 
Clustering:  introduction  similarity measures  hierarchical clustering methods  kmeans clustering methods  multidimensional scaling 
671715 
9 
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 
575644 