Statistics 210A: Theoretical Statistics (Fall 2018)
Course Information
Materials
Materials from class:
Aug. 29: demo of exponential tilting
Sep. 20: demo of Bayesian inference for the BetaBinomial distribution
Sep. 27: demo of Bayes, hierarchical Bayes, and JamesStein
Assignments:
Content
Stat 210A is Berkeley's introductory Ph.D.level course on theoretical statistics. It is a fastpaced 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
Largesample theory
Highdimensional testing
Multiple testing and selective inference
Prerequisites:
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
You must write up the problem by yourself.
You may NOT consult any solutions from previous iterations of this course.
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  RaoBlackwell 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  JamesStein paradox, confidence intervals 
Oct. 4  Secs. 5.1 and 5.2 of LehmannCasella  Minimaxity and admissibility 
Oct. 9  Secs. 12.1, 12.2, 12.3 and 12.4 of Keener  Hypothesis testing, NeymanPearson 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 likelihoodbased tests and CIs 
Nov. 20  Secs. 19.119.3 of Keener  Bootstrap and permutation tests 
Nov. 22   No class (Thanksgiving) 
Nov. 27  15.115.4 of LehmannRomano  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 

