NATIONAL CHIAO TUNG UNIVERSITY

INSTITUTE OF STATISTICS

 

MULTIVARIATE ANALYSIS

FALL 2007

 

 

 


Instructor:

Guan-Hua Huang, Ph.D.

 

Office: 423 Joint Education Hall

 

Phone: 03-513-1334

 

Email: ghuang@stat.nctu.edu.tw

Class meetings:

Tuesday 9:00-12:00 at 406 Joint Education Hall

Office hours:

By appointment

Class website:

http://www.stat.nctu.edu.tw/subhtml/source/teachers/ghuang/course/multivariate07/

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, cluster analysis, discrimination and classification, structural equation models.

 

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., 2002. Applied Multivariate Statistical Analysis, Fifth 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 probability, mathematical statistics, and linear regression.

 

METHOD OF STUDENT EVALUATION

 

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

 

COURSE OUTLINE

 

Readings refer to: Johnson, R.A. and Wichern, D.W., 2002. Applied Multivariate Statistical Analysis, Fifth Edition.

 

Module

Topic

Reading (pages)

1

Aspects of multivariate analysis:

-   introduction

-   review of linear algebra and matrices

1-30, 50-111

2

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

30-37, 67-79,

112-148

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

149-209

4

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

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)

272-307

6

Principal components:

-   introduction

-   population principal components

-   summarizing sample variation by principal components

-   large sample inferences

426-455

7

Factor analysis:

-   introduction

-   orthogonal factor model

-   methods of estimation

-   factor rotation

-   factor scores

477-524

8

Clustering:

-   introduction

-   similarity measures

-   hierarchical clustering methods

-   k-means clustering methods

-   multidimensional scaling

668-708

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

581-641

10

Structural equation models

524-529