Statistics 210B
Theoretical Statistics
Prof. Michael Jordan
Tuesday and Thursday, 12:30-2:00, 330 Evans
Spring 2006
Announcements
- May 10: The final exam will be on Friday, May 12th,
in 332 Evans from 3:30 to 5:30.
- Apr. 20: There will be no class on Tuesday, April 25th.
- Jan. 28: Note that solutions to HW1 (revised as of 1/28)
have been posted (see below).
- Jan. 26: There will be no class on Tuesday, January 31.
- Jan. 24: In the homework problems, when I say
"asymptotic distribution", I always mean that the random variables
in question should be scaled so as to yield nondegenerate limiting
distributions. The appropriate scaling for problems 3 and 5 in
Homework 1 is sqrt(n).
Topics
- Weak convergence
- Empirical processes (entropy, entropy with bracketing, chaining,
asymptotic equicontinuity, Donsker theorems)
- M-estimation
- U-statistics, Hoeffding and von Mises expansions
- Functional delta method
- Penalties and sieves
- Bootstrapping empirical processes
- Nonparametric Bayesian methods
- Semiparametric models
Prerequisites
- Statistics 210A
- Statistics 204 or 205A
Required Texts
-
A. van der Vaart, Asymptotic Statistics, Cambridge University Press, 1998.
-
D. Pollard, Convergence of Stochastic Processes, Springer-Verlag, 1984.
[pdf]
-
P. Bickel and K. Doksum, Mathematical Statistics: Vol II.
[pdf]
Supplemental Texts
-
S. A. van de Geer, Empirical Processes in M-Estimation,
Cambridge University Press, 1999.
-
P. Billingsley, Convergence of Probability Measures,
John Wiley, 1968.
-
R. J. Serfling, Approximation Theorems of Mathematical Statistics,
John Wiley, 1980.
-
D. Pollard, Empirical Processes: Theory and Applications,
Institute of Mathematical Statistics, 1990
-
A. Van der Vaart and J. Wellner,
Weak Convergence and Empirical Processes,
Springer, 1996.
Homework
Lecture Notes
Staff Office Hours and Locations