Statistics 210A: Theoretical Statistics (Fall 2020)

If you are an undergraduate who wants to take the course, please fill out the permission code request form to let me know about your background.

Anyone considering taking the course is encouraged to read the frequently asked questions regarding preparation and review materials.

Course Information

Materials

Lecture notes:

Recitation section materials:

Materials from class:

Assignments:

Content

Stat 210A is Berkeley's introductory Ph.D.-level course on theoretical statistics. It is a fast-paced and demanding course intended to prepare students for research careers in statistics.

Topics:

  • Statistical decision theory, frequentist and Bayesian

  • Exponential families

  • Point estimation

  • Hypothesis testing

  • Resampling methods

  • Estimating equations and maximum likelihood

  • Empirical Bayes

  • Large-sample theory

  • High-dimensional testing

  • Multiple testing and selective inference

References

All texts are available online from Springer Link.

Main text:

Supplementary texts:

Undergrad-level review texts for prerequisites:

Grading

Your final grade is based on:

  • Weekly problem sets: 50%

  • Final exam: 50%

Lateness policy: Homework must be submitted to Gradescope at midnight on Wednesday nights. Late problem sets will not be accepted, but we will drop your lowest two grades.

Collaboration policy: For homework, you are welcome to work with each other or consult articles or textbooks online, with the following caveats:

  1. You must write up your solution by yourself.

  2. You may NOT consult any solutions from 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 and you will be reported to the University Office of Student Conduct.

Accommodations

Students with disabilities: Please see me as soon as possible if you need particular accommodations, and we will work out the necessary arrangements.

Scheduling conflicts: Please notify me in writing by the second week of the term about any known or potential extracurricular conflicts (such as religious observances, graduate or medical school interviews, or team activities). I will try my best to help you with making accommodations, but cannot promise them in all cases. In the event there is no mutually-workable solution, you may be dropped from the class.

Lecture schedule

Date Reading Topic
Aug. 27 Chap. 1 and Sec. 3.1 of Keener Probability models and risk
Sep. 1 Chap. 2 of Keener Exponential families
Sep. 3 Chap. 2 and Sec. 3.2 of Keener Sufficient statistics
Sep. 8 Secs. 3.4, 3.5, and 3.6 of Keener Minimal sufficiency and completeness
Sep. 10 Secs. 3.6 and 4.1 of Keener Rao-Blackwell theorem
Sep. 15 Secs. 4.1 and 4.2 of Keener UMVU estimation
Sep. 17 Secs. 4.5 and 4.6 of Keener Information inequality
Sep. 22 Secs. 7.1 and 7.2 of Keener Bayesian estimation
Sep. 24 Secs. 7.1 and 7.2 of Keener Conjugate priors
Sep. 29 Secs. 7.2 and 11.1 of Keener More on Bayes
Oct. 1 Secs. 7.2 and 11.1 of Keener Hierarchical priors, empirical Bayes
Oct. 6 Secs. 11.1, 11.2 and 9.4 of Keener James-Stein paradox, confidence intervals
Oct. 8 Secs. 5.1 and 5.2 of Lehmann-Casella Minimaxity and admissibility
Oct. 13 Secs. 12.1, 12.2, 12.3 and 12.4 of Keener Hypothesis testing, Neyman-Pearson lemma
Oct. 15 Secs. 12.3, 12.4, 12.5, 12.6 and 12.7 of Keener UMP tests
Oct. 20 Secs. 13.1, 13.2, and 13.3 of Keener Testing with nuisance parameters
Oct. 22 Secs. 13.1, 13.2, and 13.3 of Keener UMP unbiased tests
Oct. 27 Secs. 13.1, 13.2, and 13.3 of Keener UMP unbiased tests
Oct. 29 Secs. 14.1, 14.2, 14.4, 14.5, and 14.7 of Keener Linear models
Nov. 3 Secs. 8.1, 8.2, and 8.3 of Keener Asymptotic concepts
Nov. 5 Secs. 8.3 and 8.4 of Keener Maximum likelihood estimation
Nov. 10 Secs. 8.5, 9.1, and 9.2 of Keener Relative efficiency
Nov. 12 Secs. 9.1, 9.2, and 9.3 of Keener Consistency of the MLE
Nov. 17 Secs. 9.1, 9.2, and 9.3 of Keener Asymptotic normality of MLE
Nov. 19 Secs. 9.5 and 9.7 of Keener Trio of asymptotic likelihood-based tests and CIs
Nov. 24 Secs. 19.1-19.3 of Keener Bootstrap and permutation tests
Nov. 26 No class (Thanksgiving)
Dec. 1 15.1-15.4 of Lehmann-Romano Bootstrap theory
Dec. 3 Lecs. 2, 3 of Candes Testing in high dimensions
Dec. 8 Lec. 6 of Candes Multiple testing
Dec. 10 Lecs. 8 and 9 of Candes Multiple testing