Course Description
Supplemental study on the methods, principles, and theory of statistical inference. This course is an adjunct to Statistical Inference and provides opportunity for additional study of the material in that course. Problems, background material, and details of derivations and proofs related to Statistical Inference content will be covered.
Athena Title
Supplemental Stat Inference
Corequisite
STAT 6820
Semester Course Offered
Offered spring
Grading System
S/U (Satisfactory/Unsatisfactory)
Course Objectives
Through this course and its co-requisite Statistical Inference, students will gain the ability to solve problems in the theory and methodology of statistical inference. 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 and statistical background material for Statistical Inference and be able to describe that background knowledge and apply it to problems in statistical inference. They will be able to identify and avoid gaps and logical flaws in mathematical arguments regarding statistical methods. Students will strengthen their understanding of how statistical theory guides statistical applications and how to use theory to choose and/or validate statistical techniques for a given problem. 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 6820 and for the departmental Ph.D.-level qualifying exams.
Topical Outline
The course will provide supplemental coverage of the topics covered in STAT 6820, which include sufficiency and other principles of data reduction, completeness, ancillarity of a statistic, point estimation, methods of estimation, maximum likelihood method, evaluation of estimators, uniformly minimum variance unbiased estimation, Cramer-Rao inequality, efficiency, hypothesis testing, Neyman-Pearson lemma, uniformly most powerful (UMP) tests, likelihood ratio tests, monotone likelihood ratio family and applications to UMP tests, interval estimation, coverage probabilities, and confidence sets.