MATH 6740: Introduction to Mathematical Statistics (spring 2009)

Instructor: Michael Nussbaum

The course will begin with a review of classical statistical theory, i.e. point estimation, hypothesis testing and confidence intervals, as well as Bayesian and minimax decisions. Though some familiarity with this basic material is mentioned among the prerequisites, an effort will be made, in case of necessity, to accommodate students having no prior formal knowledge of statistics and to make this introductory part self-contained.

The course will not focus on this classical material; rather it is intended as an introduction to modern computer intensive and nonparametric methods. This main part will begin with statistical functionals and goodness-of-fit tests, where some inequalities and limit theorems from probability will also be reviewed. Next we will discuss the theoretical basis for the bootstrap, which is a modern computer intensive method for finding tests and confidence intervals under minimal assumptions. A closely related topic is data smoothing, also known as nonparametric curve estimation. We will cover the density estimation and regression cases; an introduction to wavelet techniques will be included.

The last part of the course will deal with the connection of machine learning and statistical inference. We will present an introduction to classification and pattern recognition, as the core areas of statistical machine learning.

The continuation course Statistical Learning Theory (MATH 7740, scheduled for fall 2009) will treat this last topic in a broader perspective and in much more detail.