CPH/STAT 687 Theory of Linear Models (Spring 2015)
Syllabus: pdf
Time: MW, 1:00 – 2:15 pm
Location: Drachman A119
Instructor: Z. John Daye, PhD
Drachman Hall (bldg. 202) A226
1295 N. Martin Ave
PO Box 245211
Tucson, AZ 85724
(520) 626-3507
Office Hours: TBA
Course Description: The course will cover linear and quadratic forms, Gauss-Markov theorem, linear hypothesis tests, confidence and prediction regions, and analysis of variance. Results of linear algebra and random vectors will be reviewed. If time permits, additional topics from nonparametric regression, asymptotic expansions, robust statistics, etc. may be introduced.
Course Prerequisites: Theory of Statistics (STAT 566/MATH 566), Linear Algebra (at the level of MATH 413).
Course Learning Objectives: The course builds a solid foundation in the theory of linear models for Ph.D. students in Statistics/Biostatistics. At the end of the course, the students will be prepared to
Understand and be proficient at theoretical developments in the analysis of linear models, including linear and quadratic forms, least squares, linear hypothesis testing, analysis of variance, etc.
Apply the results from linear model theory in advanced topics, such as nonparametric models, multivariate analysis, high-dimensional inference, etc.
Read statistical/biostatistical papers involving linear model theory on their own.
Required Book:
G.A.F. Seber, A.J. Lee (2003). Linear Regression Analysis.
Reference Books:
M. Bilodeau, D. Brenner (1999). Theory of Multivariate Statistics.
R. Christensen (2002). Plane Answers to Complex Questions: The Theory of Linear Models.
F.A. Graybill (2000). Theory and Application of the Linear Model.
D.A. Harville (1997). Matrix Algebra from a Statistician's Perspective.
B. Jorgensen (1993). Theory of Linear Models.
R. Myers, J. Milton (2001). A First Course In The Theory of Linear Models.
K.B. Petersen, M.S. Pedersen (2012). The Matrix Cookbook. (www2.imm.dtu.dk/pubdb/p.php?3274)
C.R. Rao (1973). Linear Statistical Inference and Its Applications.
S.R. Searle (1997). Linear Models.
G.A.F. Seber (2008). A Matrix Handbook for Statisticians.
Lecture and Assignments:
Reading and homework problems will be given during the lecture and on webpage.