STATS 200B: Theoretical Statistics

Winter 2021

• Lectures: TR 3:30pm-4:45pm. Delivered online via Zoom. (First lecture 1/5/21)
• Links to Zoom meetings will be posted on Campuswire. To install Zoom follow this link. Please also see UCLA policy regarding protection of privacy and data when using Zoom.

• You might also find UCLA resources for remote learning useful.

• Instructor: Arash A. Amini.

• Office Hours: Thursdays 11am-1pm (starting 1/18/24). Online in Zoom.
• Announcements: Will be posted Campuswire (Use code 3774 to enroll).
• Use Gradescope for homework submission. (Code 74G3NP)

Syllabus

• Statistical decision theory: frequentist and Bayesian approaches
• Point estimation: sufficiency, Rao–Blackwell, UMVU, Cramér–Rao
• Exponential families
• Bayes risk and minimax
• M-estimation and maximum likelihood
• Asymptotic properties of estimators: consistency, asymptotic normality, delta method
• Hypothesis testing and confidence intervals
• High-dimensional inference: empirical processes, ULLNs, finite-sample bounds

Textbook

• R. W. Keener, Theoretical Statistics: Topics for a Core Course, Springer, 2010.

The electronic version of the book should be available form the publisher website (linked above) when accessed through the UCLA network. (You can use Stat. VPN if connecting from home.)

The following is a list of other closely related sources:

• P. J. Bickel and K. A. Doksum, Mathematical Statistics, Basic Ideas and Selected Topics, Vol.1, Pearson, 2006.
• E. L. Lehmann and G. Casella, Theory of Point Estimation, 2nd. Springer, 2003.
• A. W. van der Vaart, Asymptotic Statistics. Cambridge University Press, 2000.
• E. L. Lehmann and J. P. Romano, Testing Statistical Hypotheses, Springer, 2008.

Slides

Homework

Lecture videos

Prerequisites

• Upper division probability and statistics, real analysis and linear algebra.

Grading

• Homework 60%, Final 40% (Take-home)