MATH 674: Introduction to Mathematical Statistics (Spring 2004)

Instructor: Michael Nussbaum

Meeting Time & Room

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

Textbook: van der Vaart, A., Asymptotic Statistics, Cambridge University Press 1998

Other reference books:

• Shao, Jun, Mathematical Statistics, Springer Verlag, 1998 ( basic concepts of math. statistics)
• Shiryaev, A., Probability, 2nd ed. Springer Verlag, 1996 (distances of probability measures, contiguity and entire separation of sequences of p.m.)
• Lehman, E. L., Elements of Large-Sample Theory, Springer Verlag, 1998 (complement to textbook, asymptotic statistics at more basic level)

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. Some statistical distances for probability measures are introduced, like Hellinger and total variation distance and also the Kullback-Leibler relative entropy. The latter will be motivated by a discussion of source coding for information transmission. Asymptotic methods are introduced and developed in detail, with an emphasis on the concept of contiguity and its application to nonparametric hypothesis testing.

Last modified: October 23, 2003