Stat 581

Advanced Theory of Statistical Inference

• Instructor: Peter Hoff
• Lectures: MWF, 10:30-11:20, CMU 228
• Office hours: T Th 12:30-1:30 and by appointment, PDL C-319

• Homework assigned by Wednesday is due the following Monday.
• There will be two quizzes (10/23, 11/18) and a final (12/9) exam.
• The homework, two quizzes and final will count as 30%, 20%, 20% and 30% of the course grade, respectively.

• Week 10
  • Wed: Finish reading LC 3.1 and start reading LC 5.4.
  • Mon: Read LC 3.1.
• Week 9
  • Fri: Finish reading LC 3.2 and start reading LC 3.1.
  • Wed: Do exercises 8.4, 8.7 and 8.8 to be turned in Wednesday 11/27.
  • Mon: Quiz.
• Week 8
  • Fri: Read LC 3.2 and the lecture notes on invariance.
  • Wed: Read LC 3.2 and the lecture notes on invariance. Do exercises 7.6, 8.2 and 8.3 to be turned in Wednesday 11/20.
• Week 7
  • Fri: Complete the reading on minimax estimation.
  • Wed: Do exercises 7.1,7.2,7.3 and 7.4 to be turned in Wednesday 11/13.
  • Mon: Continue reading the material on minimax estimation.
• Week 6
  Fri: Start reading the notes on minimax estimation and LC 5.1.
  • Wed: Read LC 5.5 and 5.6. Do exercises 6.2, 6.3, 6.6 and 6.8 to be turned in Wednesday 11/6.
  • Mon: Read LC 4.6 and 5.4.
• Week 5
  • Fri: Do exercises 6.1, 6.4 and 6.5 to be turned in Wednesday 10/30. Start reading LC 4.6, 5.4, 5.5.
  • Wed: In class quiz - closed book, closed notes.
  • Mon: Start reading the notes on shrinkage, and study past exams and the notes to study for the quiz.
• Week 4:
  • Fri: Read the notes on conjugate priors.
  • Wed: Read LC section 4.3.
  • Mon: Do exercises 5.1, 5.3, 5.4, 5.8 and LC 4.2.2, to be turned in Monday 10/21.
• Week 3:
  • Fri: Start reading LC chapter 4 and the lecture notes on Bayesian inference.
  • Wed: Do exercise 4.8, to be turned in Monday 10/14.
  • Mon: Review NP lemma for Wednesday and do exercises 4.5, 4.6 and 4.7, to be turned in Monday 10/14.
• Week 2:
  • Wed: Do exercise 4.3, to be turned in Monday 10/7.
  • Mon: Read LC 5.7 and the notes on admissibility.
• Week 1:
  • Fri: Read the beginning of LC 5.7 and the beginning of the lecture notes on admissibility. Do exercises 3.1, 3.2, 4.1, 4.2, 4.4, to be turned in Monday 10/7.
  • Wed: Read LC 1.1, 1.2, 1.3, 1.5 and the skim the rest. You may already know some of this material.
• Week 0: Read the lecture notes on measure theory and exponential families and try the related exercises. Familiarity with this material will be assumed throughout the course.

• Theory of Point Estimation, Lehmann and Casella, 1998 (required text)
• Testing Statistical Hypotheses, Lehmann and Romano, 2005 (available online)
• Theoretical Statistics, Keener, 2010 (available online)
• Mathematical Statistics, Ferguson 1967 (very understandable)
• Statistical Decision Theory and Bayesian Analysis, Berger, 1985 (very Bayesian)

1. Basic decision theory
2. Admissibility and complete class theorems
3. Bayesian inference
4. Empirical Bayes and shrinkage
5. Minimax inference
6. Equivariant inference
7. Invariant testing
8. Unbiased tests