6.260 Theoretical Statistics
Room 32-141 (Note that the room number has changed.)
Tuesday, Thursday 2:30–4:00 PM
Instructor:
Professor Tamara Broderick
Office Hours: Tuesday & Thursday, 4–5pm, 32-G498
Email: 
TA:
Tianheng Wang
Office Hours: Monday 2–3pm & Wednesday 1–2pm, 32-D574
Email: 
Piazza Site
Announcements, homeworks, and lecture notes can be found at the Piazza site.
Description
A graduate-level introduction to theoretical statistics, covering both frequentist and Bayesian aspects of modeling, inference, and decision-making. Topics include statistical decision theory; point estimation; exponential families; Bayesian methods; empirical and hierarchical Bayes; hypothesis testing; confidence intervals; asymptotics; M-estimation; James-Stein theory; high-dimensional regression and covariance estimation.
Texts
Required: Keener (2010) Theoretical Statistics: Topics for a Core Course; Springer
Supplementary: Robert (2007) The Bayesian Choice; Springer
Outline
- Decision theory, risk (frequentist, Bayesian)
- Exponential families
- sufficiency
- completeness
- ancillarity
- Basu's Theorem
- Rao-Blackwell
- Uniformly minimum variance unbiased estimators
- bias-variance tradeoff
- normal one-sample theory
- information inequality
- Bayes theorem, Bayes estimator
- conjugacy
- Hierarchical Bayes
- empirical Bayes
- objective Bayes
- Asymptotics
- Maximum likelihood estimator asymptotics
- Robust statistics
- M-estimation
- James-Stein theory
- Laplace expansions
- High-dimensional regression
- High-dimensional covariance estimation
Prerequisites
Linear algebra, 6.436 or equivalent (upper division probability/statistics). Real analysis is a plus.
Assessment
30%: Homeworks (every other week)
30%: Midterm
40%: Final exam