Math 674 — Spring 2002 Introduction to Mathematical Statistics

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

Course homepage: www.math.cornell.edu/~nussbaum/Math674.html

Textbook: Shao, Jun, Mathematical Statistics, Springer Verlag, 1998.

Other reference books:
van der Vaart, A., Asymptotic Statistics, Cambridge University Press 1998.
Lehman, E. L., Elements of Large-Sample Theory, Springer Verlag, 1998.
Schervish, M. J., Theory of Statistics, Springer Verlag, 1995.

Abstract: The course is coordinated with OR&IE 670 to form the second part of a one-year course in mathematical statistics; familiarity with Chapters 1-3 of the textbook is thus assumed. Estimation in parametric models is the first topic; it includes Bayes decisions and estimators, minimaxity, invariance and the method of maximum likelihood. A brief introduction to Markov chain Monte Carlo is given in the context of Bayesian inference. We also discuss topics in nonparametric estimation such as empirical distribution function, density estimation, statistical functionals, robustmess, linear functions of order statistics and the bootstrap. Tests in nonparametric models are treated in connection with estimation problems. Basic concepts of decision theory are reviewed throughout the course; asymptotic methods are emphasized.