MATH 6740 - Introduction to Mathematical Statistics

Michael Nussbaum, spring 2014.

Prerequisites: MATH 6710 (measure theoretic probability) and ORIE 6700 (statistical principles), or permission of instructor.

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 will not focus on this classical material; rather it is intended as an introduction to some modern nonparametric and Bayesian methods. The course will focus on the following topics: (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.

Required Textbooks

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

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