MATH 6740: Introduction to Mathematical Statistics (Spring 2011)

Instructor: Michael Nussbaum

The course assumes some familiarity with basic statistical theory, i.e. point estimation, hypothesis testing and confidence intervals, as well as Bayesian and minimax decisions. The course will not focus on this classical material; rather it is intended as an introduction to modern computer intensive and nonparametric methods. The main part will focus on the theory of nonparametric estimation, where also some inequalities and limit theorems from probability will be reviewed. A closely related topic is data smoothing, also known as curve estimation. The density estimation and regression cases will be covered; an introduction to wavelet techniques will be included. Another possible topic is the theoretical basis for the bootstrap, a modern computer intensive method for finding tests and confidence intervals under minimal assumptions. The last part of the course will deal with the connection of machine learning and statistical inference. An introduction to classification and pattern recognition will be presented, as the core areas of statistical machine learning.