STA 732: Statistical Inference

Personnel and meeting times

  • Peter Hoff (Lecturer)
    • Lecture : Tue, Thu 10:05-11:20, Old Chemistry 025
    • Office hours: Mon, Wed 9:00-10:00 and by appointment, Old Chem 219
  • Vivek Singh (TA)
    • Office hours: Thu 4:30-6:30 Old Chem 025

Assignments

2025-01-28: Homework 3 is assigned, due in one week.

2025-01-21: Homework 2 is assigned, due in one week. Read the old notes on exponential familes or review this material in the book. Continue reading the course notes and LC 5.7.

2025-01-14: Homework 1 is assigned, due in one week. Continue reading LC 1.1, 1.7 and 5.7.

2025-01-09: Skim the review material in LC 1.2,1.3, 1.5 and 1.6 as necessary. Read LC 1.1, 1.7 and 5.7. Try some of the supplementary exercises, in particular, 1.9, 1.10, 1.12, and 2.5.

Course outline

  1. Classical decision theory:
    1. Risk, admissibility and complete class theorems;
    2. Bayes, invariant and minimax procedures;
    3. Compound risk, shrinkage and empirical Bayes.
  2. Efficient estimation:
    1. Optimal unbiased estimation (UMVUE);
    2. CAN estimation (MLE, M and Z estimation);
    3. Efficient tests and CIs.
  3. Sparse estimation:
    1. Minimax rates;
    2. Sparsistent estimation;
    3. high-dimensional problems.

References

  • Lehmann and Casella [1998] Theory of Point Estimation.
  • Lehmann and Romano [2005] Testing Statistical Hypotheses
  • Keener [2010] Theoretical Statistics: Topics for a Core Course

Evaluation

  • 33% Homework:
    • 10% per-late day penalty including weekends;
    • maximum of three one-day extensions per student.
  • 34% Quizzes
    1. Tue halfway through the semester in lecture.
    2. Tue 4/15 in lecture.
  • 33% Final 4/30 9:00-12:00 Old Chem 025