Statistics 210A: Theoretical Statistics (Fall 2018)

Course Information

  • Prof. Will Fithian (Instructor)

    • Evans 301

    • Office Hours: Tu 12:30-1:30, Th 11-12 (or by appointment)

  • Xiao Li (GSI)

    • Evans 444

    • Office Hours: M 12-1pm, Th 1-2pm

  • Lectures TuTh 9:30-11, Davis 534

  • Final Exam Tu Dec 11, 3-6pm, location TBD

  • Syllabus

  • Announcements, handouts at bCourses

  • Piazza discussion site for technical questions (no homework spoilers!)

Materials

Materials from class:

  • Aug. 29: demo of exponential tilting

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

Prerequisites:

  • Linear algebra

  • Real analysis

  • One year of upper-division probability and statistics

References

All texts are available online from Springer Link.

Main text:

Supplementary texts:

Grading

Your final grade is based on:

  • Weekly problem sets: 50%

  • Final exam: 50%

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

Collaboration policy: For homework, you are welcome 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 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.

Reading Assignments

Date Reading Topic
Aug. 23 Chap. 1 and Sec. 3.1 of Keener Probability models and risk
Aug. 28 Chap. 2 of Keener Exponential families
Aug. 30 Chap. 2 and Sec. 3.2 of Keener Sufficient statistics
Sep. 4 Secs. 3.4, 3.5, and 3.6 of Keener Minimal sufficiency and completeness
Sep. 6 Secs. 3.6 and 4.1 of Keener Rao-Blackwell theorem
Sep. 11 Secs. 4.1 and 4.2 of Keener UMVU estimation
Sep. 13 Secs. 4.5 and 4.6 of Keener Information inequality
Sep. 18 Secs. 7.1 and 7.2 of Keener Bayesian estimation
Sep. 20 Secs. 7.1 and 7.2 of Keener Conjugate priors
Sep. 25 Secs. 7.2 and 11.1 of Keener More on Bayes
Sep. 27 Secs. 7.2 and 11.1 of Keener Hierarchical priors, empirical Bayes
Oct. 2 Secs. 11.1, 11.2 and 9.4 of Keener James-Stein paradox, confidence intervals
Oct. 4 Secs. 5.1 and 5.2 of Lehmann-Casella Minimaxity and admissibility
Oct. 9 Secs. 12.1, 12.2, 12.3 and 12.4 of Keener Hypothesis testing, Neyman-Pearson lemma
Oct. 11 Secs. 12.3, 12.4, 12.5, 12.6 and 12.7 of Keener UMP tests
Oct. 16 Secs. 13.1, 13.2, and 13.3 of Keener Testing with nuisance parameters
Oct. 18 Secs. 13.1, 13.2, and 13.3 of Keener UMP unbiased tests
Oct. 23 Secs. 13.1, 13.2, and 13.3 of Keener UMP unbiased tests
Oct. 25 Secs. 14.1, 14.2, 14.4, 14.5, and 14.7 of Keener Linear models
Oct. 30 Secs. 8.1, 8.2, and 8.3 of Keener Asymptotic concepts
Nov. 1 Secs. 8.3 and 8.4 of Keener Maximum likelihood estimation
Nov. 6 Secs. 8.5, 9.1, and 9.2 of Keener Relative efficiency
Nov. 8 Secs. 9.1, 9.2, and 9.3 of Keener Consistency of the MLE
Nov. 13 Secs. 9.1, 9.2, and 9.3 of Keener Asymptotic normality of MLE
Nov. 15 Secs. 9.5 and 9.7 of Keener Trio of asymptotic likelihood-based tests and CIs
Nov. 20 Secs. 19.1-19.3 of Keener Bootstrap and permutation tests
Nov. 22 No class (Thanksgiving)
Nov. 27 15.1-15.4 of Lehmann-Romano Bootstrap theory
Nov. 29 Lecs. 2, 3 of Candes Testing in high dimensions
Dec. 4 Lec. 6 of Candes Multiple testing
Dec. 6 Lecs. 8 and 9 of Candes Multiple testing