MATH 6740 - Mathematical Statistics II

(crosslisted) STSCI 6740

Fall. 4 credits. Student option grading.

Prerequisite: MATH 6710 (measure theoretic probability) and STSCI 6730/MATH 6730, or permission of instructor.

Staff.

Focuses on the modern theory of statistical inference, with an emphasis on nonparametric and asymptotic methods. Topics include empirical Bayes and shrinkage estimators, unbiased estimation of risk, adaptive estimation, as well as oracle inequalities, a powerful concept which has applications in classification and machine learning. An optional topic is the use of Markov random fields for image restoration. The course includes a discussion of the general asymptotic theory for statistical models, as a tool for finding optimal decisions, based on the concepts of contiguity and local asymptotic normality.