MATH 6740 - Mathematical Statistics II

Michael Nussbaum, fall 2016.

Some familiarity with basic statistical theory is assumed, i.e. with point estimation, hypothesis testing and confidence intervals, as well as with the concepts of Bayesian and minimax decisions. The course is intended as an introduction to some modern nonparametric and Bayesian methods. The following topics will be treated: (1) methods of construction of estimators; (2) statistical properties (consistency, rates of convergence); (3) study of optimality of the estimators; (4) adaptive estimation, leading up to the study of oracle inequalities, a powerful concept which has also found applications in the related area of classification and machine learning; (5) Bayesian inference: modeling and computation, which will touch upon the use of Markov random fields for image restoration.

Prerequisites

MATH 6710 (measure theoretic probability) and STSCI 6730 (Mathematical Statistics I), or permission of instructor.

Required Textbooks

Keener, Robert W., Theoretical Statistics. Springer, 2010. Available as an electronic resource in the Cornell Library.

Tsybakov, Alexandre B., Introduction to Nonparametric Estimation. Springer, 2009. Available as an electronic resource in the Cornell Library.