STA 732: Statistical Inference

Syllabus for STA 732 - Statistical Inference

Course Description

This course provides a comprehensive introduction to the theory of statistical inference. We will cover both finite sample statistical decision theory (decision theory, estimation, hypothesis testing, confidence intervals) and elementary large sample theory.

Prerequisites
  • Linear algebra and real analysis.
  • A background in measure theoretic probability theory (at the level of STA 711 or equivalent).
  • A background in statistical modeling (STA 702, 721 or equivalent)
Instructor

Lasse Vuursteen (lasse.vuursteen@duke.edu)
Office Hours: Fridays, 1pm - 2pm

Teaching Assistant

Han Chen (han.chen2@duke.edu)
Office Hours: Mondays and Wednesdays, 4pm - 5pm

Course Information
Dates January 7 – April 30, 2026
Lectures Tuesdays/Thursdays 10:05–11:20am
Location Biological Sciences 155

Find the extensive syllabus here.

Lecture notes

These are work in progress, please check back here frequently for updates.

Grading

The grade is made up out of combination of these four components:

  • final exam
  • midterm
  • handwritten homework
  • popquizes

Your final grade is the maximum of:

  1. Exams only: Midterm (30%) + Final (70%)
  2. Exams + Homework: Midterm (24%) + Final (56%) + Homework (15%) + Pop Quizzes (5%)

This means homework and pop-quizes can only improve your grade, never lower it.

There will be 11 random (5-minute) pop-quizes throughout the semester, designed to encourage regular reading. Homework assignments are due at the beginning of the lecture on Thursdays. Only your best 10 homeworks/popquizes count.

Schedule

Week Date Topic Reading Exercises Homework
1 Thu Jan 8 Statistical models Syllabus + Ch 1.1 1.1, 1.2, 1.3, 1.4  
  Tue Jan 13 Sufficiency Ch 1.2 1.5, 1.6, 1.7  
2 Thu Jan 15 Decision theory Ch 1.3 1.13, 1.14, 1.15 HW 1 due
  Tue Jan 20 Unbiased estimation Ch 2 intro + Ch 2.1 up until CR LB 2.1, 2.4, 2.5  
3 Thu Jan 22 Cramer-Rao lower bound Ch 2.1 2.7, 2.8 HW 2 due
  Tue Jan 27 Invariance, equivariance Ch 2.2 2.9, 2.10, 2.11  
4 Thu Jan 29 Admissibility + High-dimensional models Ch 2.3 2.12, 2.13, 2.14, 2.15, 2.16 HW 3 due
  Tue Feb 3 Minimax estimation Ch 2.4 2.17, 2.18, 2.19  
5 Thu Feb 5 Adaptation Ch 2.4 2.20, 2.21, 2.22 HW 4 due
  Tue Feb 10 Tests of simple hypotheses Ch 3.1 3.1, 3.2, 3.3  
6 Thu Feb 12 Tests of composite hypotheses Ch 3.2 3.4, 3.5, 3.6, 3.7 HW 5 due
  Tue Feb 17 Confidence sets Ch 3.3 3.10, 3.11, 3.12  
7 Thu Feb 19 Bayes decision theory Ch 4.1 4.1, 4.2 HW 6 due
  Tue Feb 24 Complete class & minimax theorem Ch 4.2-4.3 4.3, 4.4, 4.5  
8 Thu Feb 26 Bayesian testing Ch 4.4 4.6 HW 7 due
  Tue Mar 3 Midterm Exam      
9 Thu Mar 5 Asymptotic theory intro Ch 6.1    
— Mar 10, 12 Spring Break      
10 Tue Mar 17 Stochastic Convergence Ch 6.2    
  Thu Mar 19 Convergence theorems Ch 6.3   HW 8 due
11 Tue Mar 24 The likelihood principle Ch 7.1    
  Thu Mar 26 Maximum likelihood Ch 7.2   HW 9 due
12 Tue Mar 31 Bayesian UQ Ch 7.3    
  Thu Apr 2 Misspecification Ch 7.4   HW 10 due
13 Tue Apr 7 M-estimation Ch 7.5    
  Thu Apr 9 Asymptotic efficiency Ch 7.6   HW 11 due
14 Tue Apr 14 Review      
— Thu Apr 30 Final Exam (9:00am–12:00pm)      


The schedule is tentative and subject to change depending on the pace of the class.

Additional literature
  1. Keener, R. Theoretical Statistics: Topics for a Core Course. Springer.
  2. Lehmann, E.L. and Casella, G. Theory of Point Estimation. Springer.
  3. Lehmann, E.L. and Romano, J.P. Testing Statistical Hypotheses. Springer.
  4. van der Vaart, A.W. Asymptotic Statistics. Cambridge University Press.