713—Mathematical Statistics II (3) (Prereq: STAT 712) Further development of estimation theory and tests of hypotheses, including an introduction to Bayesian estimation, sufficiency, minimum variance principles, uniformly most powerful and likelihood ratio tests, and sequential probability ratio tests.
Usually Offered: Spring Semesters
Purpose: To acquaint beginning graduate students in statistics and other disciplines with the mathematical development of statistical inference. To provide a foundation for further study in statistical theory at both the master's and doctoral levels.
Current Textbook: Statistical Inference (2nd edn.), by G. Casella and R.L. Berger. Duxbury, 2002.
|Data Reduction: Likelihood, sufficient statistics, completeness||1.5 weeks|
|Point Estimation: method of moments, maximum likelihood estimation, mean squared error, Cramer-Rao lower bound, best unbiased estimators||2.5 weeks|
|Testing Hypotheses: Test statistics, "sensible" tests, most powerful tests and the Neyman-Pearson lemma, UMP tests, monotone likelihood ratio, likelihood ratio tests||2.5 weeks|
|Confidence Intervals: pivotal quantities, test inversion, UMA intervals||2 weeks|
|Asymptotic evaluation: consistency, asymptotic efficiency, large sample inferences||1.5 weeks|
|Bayesian Methods: prior and posterior distributions, Bayes estimators, Bayesian intervals and tests||1.5 weeks|
|Decision Theory: decision rules, loss function optimality||1.5 weeks|
The above textbook and course outline should correspond to the most recent offering of the course by the Statistics Department. Please check the current course homepage or with the instructor for the course regulations, expectations, and operating procedures.