Teaching Assignment for Fall Semester  (2004/2005): 

STAT 647:  Multivariate Analysis

Pre-requisite: STAT 543 and knowledge of matrix theory.

Class Times and Venus: MWF 1pm in Coover 3126, rather than MWF 9am as originally proposed.

Text Book:  Anderson, T. W. (2003) ``An Introduction to Multivariate Statistical Analysis" (third ed), Wiley. 

Although we will follow Anderson's text closely at the beginning, new materials like copulae, which is a latest tool for modeling multivariate dependence and is getting increasing attention in finance and bioinformatics, will be covered as well.

On the preparation of Matrix theory, the appendix of Anderson lists a set of results which will be used for the course.

Course Grade will be determined by your performance on homework assignments (5-6) ( around 50%), a project presentation ( approximately 20%) and the final exam ( approximately 30%).

Homeworks will be assigned fortnightly.   

Solutions to Homework 2 part 1and part 2;  Hw3; Hw4;  Hw5; final exam.

Are working on a test that  can handle high dimensional data.

Will start EL test on the 27th of Oct.

What we have done up to 10/21/04 

Chapter 1: Matrix Theory -- Week 1,

Chapter 2: Multivariate Distributions.  (Weeks 2-4)

    2.1: General Notions of Multivariate distributions including independence  and characteristic functions;

    2.2: Multivariate normal distributions;

    2.3: Marginal distributions and independence;

    2.4: Partial and multiple correlation; 

    2.5: Elliptically contoured distributions;

Chapter 3: Estimation of the mean and covariance matrices. (week 5 - 7)

    3.1: Method of Moment Estimators, and their asymptotic normality

    3.2 Maximum Likelihood Estimation under Normal and Elliptical Contoured distributions

    3.3 Distributions of Quadratic Forms (chi-sq distributions)

    3.4 Wishart Distributions

Chapter 4: Tests for Multivariate Means  Week 8 -

    4.1: Hotelling T^2 Statistic

    4.2: Tests for the means (one and two samples , parametric and nonparametric) and their power properties under fixed (p fixed)  and high (p converges to \infty) dimensionality;

    4.3 A test which can handles high dimensional data proposed by Bai and Saranadara.

    4.4 (From Oct 27th.)   Tests based on the empirical likelihood.

Chapter 5: Copulae for Dependence Modelling