Stats 300A: Theory of Statistics

Lester Mackey, Stanford University, Fall 2015
Announcements

Course Schedule

Topics Lecture Notes Reading Problem Set Solutions
Tues. 9/22 The Big Picture; Decision Theory; Data Reduction via Sufficiency Scribed Lecture 1 TSH 1.1-1.2, 1.4; K 3.1-3.3
Optional: Modern relevance
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Thurs. 9/24 Exponential Families; Optimal Data Reduction via Minimal Sufficiency Scribed Lecture 2 K 2, 3.4-3.5 Homework 1 Solutions
Tues. 9/29 Optimal Data Reduction via Minimal Sufficiency and Completeness Scribed Lecture 3 K 3.4-3.5
Optional: No minimal sufficient statistic
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Thurs. 10/1 Optimal Data Reduction via Completeness; From Data Reduction to Risk Reduction; Optimal Unbiased Estimation Scribed Lecture 4 K 3.5-3.6, 4.1-4.2 Homework 2 Solutions
Tues. 10/6 Optimal Unbiased Estimation; Optimal Location Equivariant Estimation Scribed Lecture 5 K 4.1-4.2, 10.1-10.2
Optional: Unbiased risk estimation
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Thurs. 10/8 Optimal Location Equivariant Estimation Scribed Lecture 6 K 10.1-10.2 Homework 3 Solutions
Tues. 10/13 Location Equivariance and Risk Unbiasedness; Optimal Location-Scale Equivariant Estimation; Bayes Estimators and Average Risk Optimality Scribed Lecture 7 TPE 3.3, K 7.1
Optional: Rotation equivariance
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Thurs. 10/15 Bayes Estimators and Average Risk Optimality Scribed Lecture 8 K 7.1-7.2 Homework 4 Solutions
Tues. 10/20 Reflections on Bayes Estimators; Minimax Estimators and Worst-case Optimality Scribed Lecture 9 K 11.3, TPE 5.1 - -
Thurs. 10/22 Minimax Estimators and Worst-case Optimality Scribed Lecture 10 TPE 5.1 Practice Midterm Questions Solutions
Tues. 10/27 Minimax Estimators; Admissibility; Simultaneous Estimation Scribed Lecture 11 TPE 5.2, K 11.1-11.2 - -
Thurs. 10/29 In-class Midterm - - Homework 5 Solutions
Tues. 11/3 Neyman-Pearson Hypothesis Testing; Optimal Simple Tests via Likelihood Ratios Scribed Lecture 12 TSH 3.1-3.2 Midterm Solutions
Thurs. 11/5 Optimal Simple Tests; Optimal One-sided Tests via Monotone Likelihood Ratios Scribed Lecture 13 TSH 3.2, 3.4 Homework 6 Solutions
Tues. 11/10 Optimal Tests with Composite Nulls via Least Favorable Priors Scribed Lecture 14 TSH 3.8-3.9 - -
Thurs. 11/12 Optimal Unbiased Testing Scribed Lecture 15 TSH 4.1-4.2, 3.6 Homework 7 Solutions
Tues. 11/17 Optimal Unbiased Testing with Nuisance Parameters Scribed Lecture 16 TSH 4.3-4.4, 6.1 - -
Thurs. 11/19 Optimal Invariant Testing Scribed Lecture 17 TSH 6.1-6.3 Homework 8 Sneak Preview, Example Slides Solutions
Tues. 11/24 No Class: Thanksgiving Recess - - - -
Thurs. 11/26 No Class: Thanksgiving Recess - - - -
Tues. 12/1 Student Presentations; Computing Maximal Invariants in Stages Scribed Lecture 18 TSH 6.2 - -
Thurs. 12/3 Student Presentations; From Testing to Confidence Regions Scribed Lecture 19 K 12.4, Student Presentation Slides Practice Final Solutions
Mon. 12/7 Take-home Final Exam Distributed (at 10:00AM) - - Final Solutions
Weds. 12/9 Take-home Final Exam Due (by 10:00AM) - - - -


  • K = Keener (Theoretical Statistics: Topics for a Core Course)

  • TSH = Testing Statistical Hypotheses

  • TPE = Theory of Point Estimation