STAT 443/851 Theory of Linear Models

Catalogue description

A rigorous examination of the general linear model using vector space theory. Includes: generalized inverses; orthogonal projections; quadratic forms; Gauss-Markov theorem and its generalizations; BLUE estimators; Non-full rank models; estimability considerations.

Prerequisite(s): MATH 164 (formerly MATH 264) or MATH 266, STAT 342, and STAT 344 or 345.

My description

This course is a rigorous examination of the general linear models using vector space theory, in particular the approach of regarding least square as projection. The topics includes: vector space; projection; matrix algebra; generalized inverses; quadratic forms; theory for point estimation; theory for hypothesis test; theory for non-full-rank models.

1. Introduction to Linear Models

2. Vector Space and Projection

3. Matrix Algebra

4. Multivariate Normal Distribution

5. Distribution of Quadratic Form (Sum Squares)

6. Point Estimation for Linear Models

7. Hypothesis Testing for Linear Models

8. Theory for Non-full-rank Linear Models

Acknowledgements

The lectures were built upon the lecture notes for stat 8260 by Danniel Hall and the textbook LINEAR MODELS IN STATISTICS, Second Edition, by Alvin C. Rencher and G. Bruce Schaalje, ISBN 978-0-471-75498-5 (cloth)

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