STAT 2661

Linear Models Theory I

Fall 2009

Instructor: Allan Sampson,

CL2701

624-8372

email: asampson@pitt.edu

Textbooks: A First Course in Linear Model Theory by Ravishanker and Dey (2002 CRC Press).

SAS for Linear Models (4th Ed) by Littel, Stroup and Freund (Students should have this from STAT2132)

Material:

This course will provide the basic results for linear model theory using a coordinate free geometric approach. Numerical linear algebra methods will be taught which provide the bridge from theory to standard analysis approaches as exemplified by those in SAS PROC GLM. Much of the material covered in class will come from the instructors notes which will be provided to the students and the text will be used for supplementary readings and elaborations.

Grading: There will be assignments on most weeks, a midterm exam and a final. They will count toward the grade as follows:

Assignments 35%; Midterm 25%; Final 40%

Exams: The midterm exam and final exam will be announced in class. The midterm will be announced two weeks before it is to occur.

Abbreviated Course Outline and Related References

1. Matrices and Linear Algebra ( Review, projection theorems, idempotent matrices, and misc.)

2. Distribution Theory (Review of univariate distributions, multivariate normal (singular and non-singular), noncentral distributions, quadratic forms, distribution of projections, Cochran's Theorem, independence of linear and quadratic forms, probability inequalities, Bonferroni, PLOD, more PLOD, misc inequalities.)

3. Generalized Inverses (Definitions and basic results, solutions to systems of equations, techniques for obtaining generalized inverses, explicit computations and projection matrices, computer applications.)

4. Linear Models (Lse's, NE's, design matrices and linear spaces, estimation, Gauss-Markov Theorem, distribution theory for estimators, fundamental theorems of hypothesis testing, computer package approaches, computer applications.)

5. Other GLM Considerations (Simultaneous inference, Scheffe, Bonferrroni, PLOD, more PLOD, robustness, error diagnostics).

6. One-way Layout (Coordinate free and parametrized, estimators and ANOVA table, specific simultaneous inference procedures.)

7. Two-way layout (Coordinate free and parametrized, one observation per cell, nonorthogonality, computational issues.)

8. Misc topics

References:

Linear Models by Searle

Analysis of Messy Data Vol 1 and Vol 3 by Milliken and Johnson

Linear Statistical Inference and Its Applications by CR Rao

Generalized Inverse of Matrices by Rao and Mitra

Regression and the Moore-Penrose PseudoInverse by Albert

Matrix Algebra Useful for Statisticians by Searle

Generalized Linear and Mixed Models 2nd Ed by McCulloch and Searle

Plane Answers to Complex Questions by Christensen

Theory and Application of the Linear Model by Graybill