STATS 200B -- Theoretical Statistics

Winter 2024

  • Lectures: TR 2pm-3:15pm @ ROYCE 160

  • Instructor: Arash A. Amini.
    • Office Hours: Thursdays 11am-1pm (starting 1/18/24).
  • TA: TBA.

  • Final Exam: TBA.

  • Announcements: Will be posted Campuswire (Use code 1646).
  • Use Gradescope for homework submission. (Code 8EBYPD)

Please read!

  • Notice: Please do not email me your late homework. Instead, post a note on Campuswire (it can have attachments) and set the visibility to TAs and Instructors only. We will address the issue there. Only requests through Campuswire are considered.

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

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.

Homework and slides

  • Homework and slides will be posted in the following Box folder.

Lecture videos

Prerequisites

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

Grading

  • Homework 60%, Final 40% (Take-home)