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MATH 503 - Mathematical Statistics |

This is a first course in the mathematical theory of statistical inference. The emphasis is on classical methods, with appropriate attention also to Bayesian methods. Topics include principles of data reduction (sufficiency and sufficient statistics, likelihood, invariance); point estimation (method of moments, maximum likelihood, Bayes estimators) and associated criteria (mean squared error, unbiasedness, consistency); some asymptotic properties of point estimators; construction of and criteria for hypothesis tests (error probabilities and power, most powerful tests, bias); asymptotics of some large sample tests; construction of and criteria for interval estimate; and elements of decision theory and applications to statistical inference (Bayes rules, minimax). Text: Statistical Inference, by G Casella and R Berger, Cengage Learning; 2nd edition (June 18, 2001). Restrictions: Must be enrolled in one of the following Levels: MN or MC Graduate Must be enrolled in one of the following Majors: Mathematics and Statistics 3.000 Credit hours 3.000 Lecture hours 0.000 Lab hours Levels: MN or MC Graduate, Undergraduate Schedule Types: Lecture Mathematics Department |