Linear Models and Multivariate Analysis

Syllabus Details

• Unit I:(Multivariate Normal Vector) Definition, linear transformation, characteristic function, Fisher-Cochran theorem, quadratic forms.
• Unit II:(Gauss-Markov Model) Gauss-Markov model with uncorrelated error, Gauss-Markov theorem, estimability and identifiability, hypothesis testing of testable hypotheses, ANOVA, variance component analysis, regression, tests for model parameters.
• Unit III:(Generalized Linear Models) GLM with non-uncorrelated error, both known and unknown; logistic regression, probit model, Cox proportional hazard model.

Course Learning Objective

1. Discuss the important theorems and concepts in multivariate analysis.
2. Apply multivariate techniques appropriately and draw appropriate conclusions.
3. Apply advanced algebraic techniques in the inference of linear models.
4. Discuss the concept of generalized least squares.
5. Discuss the exponential family of distributions and apply likelihood based inference for such a family.
6. Apply the concepts of generalized linear models to real life problems.

Recommended Books

1. Anderson, T. W. An Introduction to Multivariate Statistical Analysis. Wiley, 1984
2. Johnson, Richard A. and Wichern, Dean W. Applied Multivariate Statistical Analysis. 5th ed. Prentice-Hall, 1982
3. Sengupta, Debasis and Jammalamadaka, S. Rao. Linear Models: An Integrated Approach. World Scientific, 2003
4. Rao, C. R. Linear Statistical Inference and its Applications. 2nd ed. Wiley, 1973
5. McCullagh, Peter and Nelder, John A. Generalized Linear Models. Chapman & Hall, 1990
6. Dobson, Annette J. An Introduction to Generalized Linear Models. Chapman & Hall, 2002