Sta 732 - Statistical Inference, Spring 2023

Course description

This class will cover finite sample theory of statistical inference – including estimation, hypothesis testing, and confidence intervals – and elementary large sample theory. Specific topics (depending on time may or may not be able to cover all but aim to) include: statistical models; sufficiency; applications to exponential families, group families, and nonparametric families; minumum risk unbiased estimation; minimum risk equivariant estimation; Cramer-Rao Inequality; loss and risk functions; Bayes estimation; minimax estimation; admissibility; shrinkage estimators; Neyman-Pearson theory for hypothesis testing; confidence intervals; uniformly most powerful test and uniformly most accurate confidence intervals; asymptotic relative efficiency; maximum likelihood estimation; Wald, score, and likelihood-ratio tests; delta method; asymptotic distribution of quantiles and trimmed means.

Acknowledgement: This course contains materials such as lecture slides, homework and datasets that were developed or adapted from STA210A at UC Berkeley by Michael Jordan and Will Fithian, STA300A at Stanford by Dominik Rothenhaeusler.


STA 250 or STA 611, STA 711, linear algebra, undergraduate level real analysis

Class info


Yuansi Chen


Christine Shen

Main References

Main text:

Undergraduate review textbook:

Sta711 review textbook:

Other resources:

Lecture Timeline

Tentative, please refresh for the latest version

Date Required Reading Topic Slides Other
Jan. 11 Chap.1.1, 1.2 of Lehmann and Casella / Chap 3.1 of Keener Course introduction lecture01 review 711
Jan. 16 - No class holiday
Jan. 18 Chap. 2 of Keener Exponential families lecture02 hw00 due & hw01 out
Jan. 23 Chap. 2 - 3.4 of Keener Sufficient statistics lecture03
Jan. 25 Chap. 3.4 - 3.6 of Keener Completeness, Basu thm lecture04 hw01 due & hw02 out
Jan. 31 Chap. 3.6 - 4.1 of Keener Rao-Blackwell thm, UMVU lecture05
Feb. 01 Chap. 4.2, 4.5, 4.6 of Keener More on bias, Information inequality lecture06 hw02 due & hw03 out
Feb. 06 Chap. 10.1 of Keener Equivariance lecture07
Feb. 08 Chap. 10.2 of Keener Equivariance estimation lecture08 hw03 due & hw04 out
Feb. 13 Chap. 7.1, 7.2 of Keener Bayesian estimation lecture09
Feb. 15 Chap. 4.1 of Lehmann and Casella Bayes pros and cons lecture10 hw04 due & hw05 out
Feb. 20 Chap. 15.1, 11.1-2 of Keener Empirical Bayes and Hierarchical Bayes lecture11 sample midterm
Feb. 22 Chap. 5.1-2 of Lehmann and Casella Minimax optimality lecture12 hw05 due & hw06 out
Feb. 27 Midterm review
Mar. 01 Midterm
Mar. 06 Chap. 5.1-2 of Lehmann and Casella Minimax optimality + Minimax estimators lecture13
Mar. 08 Chap. 8.1-2 of Keener Large sample theory basics lecture14 hw06 due & hw07 out
Mar. 13 Spring break
Mar. 15 Spring break
Mar. 20 Chap. 8.3, 8.5, 9.2, 9.3 of Keener Asymptotic of MLE lecture15
Mar. 22 Chap. 8.3, 8.5, 9.2, 9.3 of Keener Asymptotic of MLE, cont hw07 due & hw08 out
Mar. 27 Chap. 12.1-4 of Keener Hypothesis testing & Neyman-Pearson paradigm lecture16
Mar. 29 Chap. 12.3-7 of Keener UMP lecture17 hw08 due & hw09 out
Apr. 03 Chap 3.6, 3.7 of Lehmann and Romano UMP in two-sided testing? lecture18
Apr. 05 Chap 3.8 of Lehmann and Romano Least favorable distributions lecture18-19 hw09 due & hw10 out
Apr. 10 Chap 4 of Lehmann and Romano UMPU lecture20
Apr. 12 Chapt. 13.1-3 of Keener UMPU in multiparam exp family lecture21 hw10 due & hw11 out
Apr. 17 Chapt. 14.5-8 of Keener Testing in general linear model lecture22
Apr. 19 Chapt. 17.1-4 of Keener Large-sample LRT & final review lecture23 hw11 due
Apr. 24 graduate reading
Apr. 26 graduate reading
May. 01 final exam

Required workload

Grading Policy

Other Course Policies

During Class

I understand that the electronic recording of notes might be important for class and so computers will be allowed in class. Please refrain from using computers for anything but activities related to the class. Phones are prohibited as they are rarely useful for anything in the course. Eating and drinking are allowed in class but please refrain from it affecting the course.

Academic Integrity and Honesty

Duke University is a community dedicated to scholarship, leadership, and service and to the principles of honesty, fairness, respect, and accountability. Citizens of this community commit to reflect upon and uphold these principles in all academic and non-academic endeavors, and to protect and promote a culture of integrity. Cheating on exams and quizzes, plagiarism on homework assignments and projects, lying about an illness or absence and other forms of academic dishonesty are a breach of trust with classmates and faculty, violate the Duke Community Standard, and will not be tolerated. Such incidences will result in a 0 grade for all parties involved as well as being reported to the Office of Student Conduct. Additionally, there may be penalties to your final class grade. Please review the Duke Academic Dishonesty policies.

Accommodations for Disabilities

Students with disabilities who believe they may need accommodations in this class are encouraged to contact the Student Disability Access Office at (919) 668-1267 as soon as possible to better ensure that such accommodations can be made.