MULTIVARIATE
ANALYSIS
FALL 2010
Instructor: 
GuanHua Huang, Ph.D. 

Office: 423 Joint Education Hall 

Phone: 035131334 

Email: ghuang@stat.nctu.edu.tw 
Class meetings: 
Tuesday 9:0012:00 at 407 Joint Education Hall 
Office hours: 
By
appointment 
Class website: 

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 