Cornell Math - MATH 674, Spring 2007

MATH 674: Introduction to Mathematical Statistics (Spring 2007)

Instructor: Michael Nussbaum

Meeting Time & Room

4 credits. Prerequisites: MATH 671 (measure theoretic probability) and OR&IE 670, or permission of instructor.

Required textbooks:

• Wasserman, L., All of Statistics. A Concise Course in Statistical Inference. Springer Verlag, 2004.
• Course packet:   Nussbaum, M., Selected Topics in Mathematical Statistics. Cornell University, 2006.

Optional textbook: Wasserman, L., All of Nonparametric Statistics, Springer, New York 2006.

Abstract: Topics include an introduction to the theory of point estimation, hypothesis testing and confidence intervals, consistency, efficiency, and the method of maximum likelihood. Basic concepts of decision theory are discussed; the key role of the sufficiency principle is highlighted and applications are given for finding Bayesian, minimax and unbiased optimal decisions. Modern computer intensive methods like the bootstrap will receive some attention, as well as simulation methods involving Markov chains. The parallel development of some concepts of machine learning will be exemplified by classification algorithms. An optional section may include nonparametric curve estimation and elements of large sample asymptotics.