Statistics 210B: Theoretical Statistics

Statistics 210B
Theoretical Statistics

Prof. Michael Jordan
Tuesday and Thursday, 12:30-2:00, 330 Evans
Spring 2007

I will not have office hours on Thursday, 4/26. If you'd like to meet with me please contact me via email.
The final exam is scheduled for Weds, May 16, from 5:00-8:00 in 330 Evans.
I will not have office hours on Thursday, 3/22. If you'd like to meet with me please contact me via email.
See below for a new section on reading assignments.
I am moving my office hours from Tuesdays at 2:00 to Thursdays at 2:00, starting Feb 20.
There will be no class on Tuesday, January 30.
Some of you asked about Problem 4 on Homework 1. The problem is correct as stated, although it needs the following clarifying remark: The random variable $X$ is assumed to be distributed according to the distribution with density $p_n$. (One purported counterexample was the case in which p_n = q_n, which yields L_n = 1, which it was claimed is not uniformly tight. L_n = 1 is indeed uniformly tight; indeed, there's nothing more tight than a sequence in which each random variable piles up all its mass at the same point). A hint that you might find useful: Use Markov's inequality.

Weak convergence
Empirical processes (entropy, entropy with bracketing, chaining, asymptotic equicontinuity, Donsker theorems)
M-estimation
U-statistics, Hoeffding and von Mises expansions
Contiguity, convergence of experiments
Asymptotic efficiency
Functional delta method
Bootstrapping empirical processes
Penalties and sieves
Semiparametric models

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.

Jan. 16: Chap. 2 of van der Vaart; Chap. III of Pollard [opt].
Jan. 18: Chap. 3 of van der Vaart
Jan. 23: Secs. 11.1, 11.2, 11.3, 12.1 and 12.2 of van der Vaart
Jan. 25: Secs. 11.1, 11.2, 11.3, 12.1 and 12.2 of van der Vaart
Feb. 1: Secs. II.1 and II.3 of Pollard.
Feb. 6: Secs. II.3 and II.4 of Pollard.
Feb. 8: Secs. II.4 and II.5 of Pollard.
Feb. 13: Sec. II.5 of Pollard.
Feb. 15: Secs. 5.1 and 5.2 of van der Vaart.
Feb. 20: Chap. 18 of van der Vaart, Secs. IV.1 and IV.2 of Pollard.
Feb. 22: Secs. V.1 and V.2 of Pollard.
Feb. 27: Sec. VII.1 and VII.2 of Pollard.
Mar. 1: Sec. VII.3, VII.4 and VII.5 of Pollard; Secs. 19.1 and 19.2 of van der Vaart [opt].
Mar. 6: Secs. 19.4 and 5.3 of van der Vaart.
Mar. 8: Secs. 7.1 and 7.2 of van der Vaart.
Mar. 13: Chap. 6 of van der Vaart.
Mar. 15: Chap. 6 of van der Vaart.
Mar. 20: Secs. 13.1 and 13.2 of van der Vaart.
Mar. 22: Chap. 14 of van der Vaart.
Apr. 3: Secs. 7.3 and 15.1 of van der Vaart.
Apr. 5: Secs. 15.2 and 15.4 of van der Vaart.
Apr. 10: Secs. 16.1 and 16.3 of van der Vaart.
Apr. 12: Secs. 16.4, 16.5, 8.1 and 8.2 of van der Vaart.
Apr. 17: Secs. 8.3 and 8.4 of van der Vaart.
Apr. 19: Secs. 8.5 and 8.9 of van der Vaart.
Apr. 24: Chap. 20 of van der Vaart.