Statistics 210B
Theoretical Statistics

Topics

• U-statistics, Hájek projections
• Concentration inequalities, the entropy method
• Empirical processes (metric entropy, chaining, asymptotic equicontinuity)
• High-dimensional covariance matrix estimation
• High-dimensional regression
• Minimax lower bounds
• Functional delta method
• Theory of the bootstrap

Prerequisites

• Statistics 210A
• Statistics 204 or 205A

Homework and Exams

Students will be required to complete regular homework assignments. These must be turned in on time to receive credit. Also, there will be a final exam. The homeworks will count for 40% of the grade and the final will count for 60% of the grade.

Lateness policy: Late problem sets will not be accepted, but you will get to drop one grade.

Collaboration policy: For homework, you are allowed to work with each other or consult articles or textbooks online, but

1. You must write up the problem by yourself.

2. You may NOT consult any solutions for previous iterations of this course.

3. If you collaborate or use any resources other than course texts, you must acknowledge your collaborators and the resources you used.

Academic integrity: You are expected to abide by the Berkeley honor code. Violating the collaboration policy, or cheating in any other way, will result in a failing grade for the semester.

Required Texts

M. Wainwright, High-Dimensional Statistics: A Non-Asymptotic Viewpoint, 2017.

Supplemental Texts

• A. van der Vaart, Asymptotic Statistics, Cambridge University Press, 1998.
• D. Pollard, Convergence of Stochastic Processes, Springer-Verlag, 1984. [pdf]
• A. Van der Vaart and J. Wellner, Weak Convergence and Empirical Processes, Springer, 1996.
• 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. Tsybakov, Introduction to Nonparametric Estimation, Springer, 2010.

Reading Assignments

• Tues, Jan 17th: lecture notes
• Thurs, Jan 19th: lecture notes
• Tues, Jan 24th: Wainwright, Chapter 1 and Section 2.1
• Thurs, Jan 26th: Wainwright, Section 2.1
• Tues, Jan 31st: Wainwright, Sections 2.2 and 2.3
• Thurs, Feb 2nd: Wainwright, Sections 2.2 and 2.3
• Tues, Feb 7th: lecture notes
• Thurs, Feb 9th: lecture notes
• Tues, Feb 14th: lecture notes
• Thurs, Feb 16th: Wainwright, Section 3.1
• Tues, Feb 21st: Wainwright, Chapter 4
• Thurs, Feb 23rd: Wainwright, Chapter 4
• Tues, Feb 28th: Wainwright, Section 5.1
• Thurs, Mar 2nd: Wainwright, Sections 5.2 and 5.3
• Tues, Mar 7th: Wainwright, Sections 5.3 and 5.4
• Thurs, Mar 9th: Wainwright, Sections 5.4 and 5.5
• Tues, Mar 14th: Wainwright, Sections 6.1 and 6.2
• Thurs, Mar 16th: Wainwright, Section 6.3
• Tues, Mar 21th: Wainwright, Section 6.5
• Thurs, Mar 23rd: Wainwright, Section 7.1
• Tues, Mar 28th: Wainwright, Section 7.2
• Thurs, Mar 30th: Wainwright, Sections 7.2 and 7.3
• Tues, Apr 4th: Wainwright, Sections 7.3 and 7.4
• Thurs, Apr 6th: Wainwright, Sections 13.1 and 13.2
• Tues, Apr 11th: Wainwright, Section 13.2
• Thurs, Apr 13th: Wainwright, Section 13.2
• Tues, Apr 18th: Wainwright, Section 13.3
• Thurs, Apr 20th: Wainwright, Section 15.1
• Tues, Apr 25th: Wainwright, Section 15.2
• Thurs, Apr 27th: Wainwright, Section 15.3

Staff Office Hours and Locations

• Prof. Michael Jordan
  Tues 12:30pm-1:30pm and Thurs 12:30pm-1:30pm in 427 Evans
  jordan@stat

• Ahmed El Alaoui
  Tues 10am-11am and Weds 11am-12pm in 428 Evans
  elalaoui@berkeley.edu

• Horia Mania
  Mon 1pm-2pm and Thurs 10am-11am in 428 Evans
  horiamania@gmail.com