STT 867: Linear Model Methodology

This course is intended for doctoral students in statistics or closely related fields. The main focus is on the fundamental principles and theory of linear regression models. The course will cover classical estimation and inference theory, as well as some more recent topics, including

• Least squares, Gauss–Markov Theorem and extensions
• Hypothesis testing and confidence region
• Simultaneous confidence intervals
• Less-than-full-rank linear models
• Estimable/Testable linear functions
• Distributional properties of quadratic forms
• Model selection and prediction
• Shrinkage methods