STAT 647:  Multivariate Analysis

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

Class Times and Venus:  Tuesday 12:40-2 pm, Wed. 12:10 -- 1:25pm  at Snedecor 319

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, new materials like missing data, copulas, high dimensional data, latent variables as well as the empirical likelihood will be covered.

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 (4) ( around 40%), a project presentation ( approximately 20%) and the final exam ( approximately 40%).   

The following are the topics which have been or will be covered.

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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. Inference for Missing Data.   (from 11/08 ) 

5.1. Missing Mechanisms  and Propensity score: Ignorable Missing at Random and Non-ignorable missing at random

5.2. A general (parametric) likelihood based framework for missing values under Missing at Random; and weighted estimation by propensity scores.

5.3.  Imputation methods:   mean imputation and multiple imputation under a Baysian framework; nonparametric multiple imputation

5.4.  Semiparametric and Nonparametric inference with and without surrogates for the missing values.  (semiparametric efficiency,  double robustness, comparasion of various inference methods.) 

Chapter 6. Inference with Latent variables.