Course Description
The theory of statistical inference is presented at an advanced level, including both frequentist and Bayesian perspectives. This course provides justification of many statistical procedures routinely used in good practice of statistics and discusses principles and theory that can be used to derive reasonable solutions to new statistical problems.
Athena Title
ADV STAT INFER I
Prerequisite
STAT 6820
Pre or Corequisite
STAT 8170
Semester Course Offered
Offered spring
Grading System
A - F (Traditional)
Course Objectives
Students successfully completing this course are expected to learn about the two principal approaches in statistics: Bayesian and frequentist. They will also learn various principles of statistical inference that can help select an appropriate statistical method in pursuing good practice of statistics. This course will teach them how to obtain appropriate statistical procedures that can be used in statistical problem solving. Training provided in this course will be crucial for dissertation research.
Topical Outline
The course will cover the following topics: sufficiency and Factorization Theorem, completeness, Basu's Theorem and its applications, elements of decision theory, Bayes rules, Bayes risk, minimax principle, Bayes estimates based on squared error and absolute error loss, Generalized Rao-Blackwell Theorem, generalized Bayes and minimax decision rules, James-Stein estimation, James-Stein estimators as empirical Bayes estimators, consistency and asymptotic normality of maximum likelihood estimators, concepts of estimating functions, principles and applications of likelihood ratio (LR) tests, asymptotic distribution of LR statistic, Neyman-Pearson Lemma, most powerful and uniformly most powerful (UMP) tests, monotone LR family and applications to UMP tests, uniformly most accurate confidence sets.
Syllabus
Public CV