Stat 210B

Spring 2013

Theoretical Statistics

Announcements:

Tue, May 7:: Homework 5 solutions have been posted here.

People:

			Office hours
Instructor	Peter Bartlett	bartlett@stat	Evans 399, Tue 1-2pm, Wed 1:30-2:30.
GSI	Siqi Wu	siqi@stat	Evans 307, Mon 3:30-4:30pm, Tue 3:30-4:30pm.

Lectures: 332 Evans. Tue/Thu 11:00 - 12:30.

Syllabus:

The course will cover a range of advanced topics in theoretical statistics, including:
Stochastic convergence. Projections. U-statistics.
Concentration inequalities. Uniform laws. Empirical process theory.
Delta method. Functional delta method.
Contiguity. Local asymptotic normality.
Efficiency of estimators. Efficiency of tests.
Nonparametric regression. Nonparametric density estimation.
M-estimators. Bootstrap estimators.

Text:

Asymptotic Statistics. Aad van der Vaart. Cambridge. 1998.
Convergence of Stochastic Processes. David Pollard. Springer. 1984. Available on-line at http://www.stat.yale.edu/~pollard/1984book/.

Prerequisites:

Stat 210A and either Stat 205A or Stat 204.

Assessment:

Homework Assignments (60%): posted on the website.
Final Exam (40%): scheduled for Thursday, 5/16/13, 8-11am, in Evans 334.

Homework Assignments:

	Due	Solutions
Homework 1: pdf	Thursday, February 7	pdf
Homework 2: pdf	Thursday, February 21	pdf
Homework 3: pdf	Thursday, March 7	pdf
Homework 4: pdf	Tuesday, April 9	pdf
Homework 5: pdf	Thursday, May 2	pdf

Lectures:

Tue, Jan 22	Organizational issues. Course outline. Stochastic convergence.	1notes.pdf. vdV 1, 2
Thu, Jan 24	Stochastic convergence. Concentration inequalities.	2notes.pdf. vdV 2. Metric Characterization of Random Variables and Random Processes. Buldygin and Kozachenko. 2000. Concentration inequalities. Boucheron, Lugosi, Bousquet. 2004.
Tue, Jan 29	Concentration inequalities.	3notes.pdf
Thu, Jan 31	Concentration inequalities.	4notes.pdf
Tue, Feb 5	U-statistics	5notes.pdf. vdV 12
Thu, Feb 7	U-statistics. Projections.	6notes.pdf. vdV 11, 12 A class of statistics with asymptotically normal distribution. Hoeffding. Ann. Math Statist. 19(3), 1948: 293-325.
Tue, Feb 12	U-statistics. Projections.	7notes.pdf. vdV 11, 12
Thu, Feb 14	Uniform laws of large numbers.	8notes.pdf. PII (esp. II.3).
Tue, Feb 19	Uniform laws of large numbers.	9notes.pdf. PII.
Thu, Feb 21	Uniform laws of large numbers.	10notes.pdf. PII Notes on Rademacher averages: A few notes on statistical learning theory. Mendelson. Rademacher and Gaussian complexities: risk bounds and structural results. Bartlett and Mendelson.
Tue, Feb 26	Uniform laws of large numbers. Metric entropy.	11notes.pdf. PII.
Thu, Feb 28	Uniform laws of large numbers. Metric entropy.	12notes.pdf. PII.
Tue, Mar 5	Uniform laws of large numbers. Metric entropy.	13notes.pdf. PII.
Thu, Mar 7	Uniform laws of large numbers. Metric entropy.	14notes.pdf. PII.
Tue, Mar 12	M-estimators. Consistency of M-estimators.	15notes.pdf. vdV5.
Thu, Mar 14	M-estimators. Consistency of M-estimators. Delta method.	16notes.pdf. vdV3, vdV5.
Tue, Mar 19	Asymptotic equicontinuity.	17notes.pdf. vdV5, vdV18, vdV19, PVII.
Thu, Mar 21	Donsker classes.	18notes.pdf. vdV18, vdV19, PVII.
Tue, Mar 26	Spring
Thu, Mar 28	Break
Tue, Apr 2	Functional delta method.	19notes.pdf. vdV20, vdV21.
Tue, Apr 9	Functional delta method. Quantile estimates.	20notes.pdf. vdV20, vdV21.
Thu, Apr 11	Contiguity. Le Cam's lemmas.	21notes.pdf. vdV6.
Tue, Apr 16	Local asymptotic normality.	22notes.pdf. vdV7.
Thu, Apr 18	Local asymptotic normality. Relative efficiency of tests.	23notes.pdf. vdV7. vdV14.
Tue, Apr 23	Relative efficiency of tests.	24notes.pdf. vdV14.
Thu, Apr 25	Relative efficiency of tests. Likelihood ratio tests.	25notes.pdf. vdV14, vdV15.
Tue, Apr 30	Likelihood ratio tests.	26notes.pdf. vdV15.
Thu, May 2	Nonparametric regression. Bootstrap estimators.	27notes.pdf. Some applications of concentration inequalities to statistics. Massart. (see Section 4.2) Local Rademacher complexities. Bartlett, Bousquet, Mendelson. Local Rademacher complexities and oracle inequalities in risk minimization. Koltchinskii vdV23.