Course Description
Supplemental study on the theory of linear models and its relevance to applications. This course is an adjunct to Theory of Linear Models and provides opportunity for additional study of the material in that course. Problems, background material, and details of derivations and proofs related to Theory of Linear Models content will be covered.
Athena Title
Supplemental Theory Linear Mod
Corequisite
STAT 8260
Semester Course Offered
Offered spring
Grading System
S/U (Satisfactory/Unsatisfactory)
Course Objectives
Through this course and its co-requisite Theory of Linear Models, students will gain the ability to solve problems in the theory of linear models. They will understand proofs of theoretical results and be able to reproduce the steps of those arguments rigorously and completely. They will strengthen their understanding of relevant mathematical material (e.g., linear algebra and the theory of matrices and vector spaces) and statistical background material (e.g., applied regression and analysis of variance) for Theory of Linear Models and be able to describe that background knowledge and its relevance to problems in linear models. They will be able to identify and avoid gaps and logical flaws in mathematical arguments regarding linear models and related methods of statistical inference. Students will strengthen their understanding of how linear model theory and the theory of matrices and vector spaces guide the practical application of the linear model. They will improve their ability to use statistical reasoning to solve problems and to communicate clearly in technical and non-technical terms about statistical methods and their applications. The course will provide useful preparation for assessments in STAT 8260 and for the departmental Ph.D.-level qualifying exams.
Topical Outline
The course will provide supplemental coverage of the topics covered in Theory of Linear Models, which include review of linear algebra, classical distribution theory, the full rank linear model, ordinary least squares, maximum likelihood estimation, the Gauss-Markov Theorem, inference in the full rank model, non-spherical covariance structure and generalized least squares estimation, non-full rank models and related concepts and techniques (estimability, reparametrizations, constraints), optimal prediction, mixed-effect models, variance components, restricted maximum likelihood estimation, and inference in the linear mixed-effect model.