Statistics 210B
Theoretical Statistics
Prof. Michael Jordan
Tuesday and Thursday, 12:30-2:00, 330 Evans
Spring 2007
Announcements
- 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.
Topics
- 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
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
Lectures
Reading Assignments
- 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.
Staff Office Hours and Locations