STAT 647: Multivariate Analysis

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

Class Times and Venus: Tuesday and Thursday: 12:40-2 pm at Sweeney 1160.

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

Although we will follow Anderson's text at the beginning, high dimensional multivariate analysis will be explored in the second half of the course.

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

Course Grade will be determined by homework assignments (4), a project presentation and possibly a final big assignment.

The following were the topics covered in 2008 (with the old dates of progress)

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Chapter 1: Multivariate Distributions. (end on 09/13)

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

1.2: Multivariate normal distributions;

1.3: Marginal distributions and independence;

1.4: Partial and multiple correlation;

1.5: Elliptically contoured distributions;

Chapter 2: Copulae for Dependence Modelling (start on 09/19 for 3 lectures)

Chapter 3: Estimation of the mean and covariance matrices. (from 09/26 )

3.1: Method of Moment Estimators, and their asymptotic normality under both fixed and increasing (high) dimensions

3.2 Maximum Likelihood Estimation under Normal and Elliptical Contoured distributions

3.3 Distributions of Quadratic Forms (chi-sq distributions)

3.4 Wishart Distributions

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Chapter 4: Tests for Multivariate Means (from 10/17)

4.1: Hotelling T^2 Statistic

4.2: Tests for the means (one and two samples , parametric and nonparametric) (10/18)

4.3 Tests for Means with high dimensional data (10/22)

4.4. A New Test which works for large p-small n (10/31)

4.5 Multiple Testing Procedure: Family Wise Error Rate and False Discover Rate. (11/07)

Chapter 5:
High Dimensional Inference for Mean and Covariance Matrices.

5.1
Difficulties with the conventional sample covariance

5.2 Threshloding
methods

5.3 Estimation of Covariance

5.4 Tests for Covariance Structure.