STA 732 - Theoretical statistics (Spring 2024)

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.

Prerequisites

Instructor

Li Ma
Email: myfirstname DOT mylastname AT duke DOT edu (Please replace ‘‘myfirstname’’ with ‘‘li’’ and ‘‘mylastname’’ with ‘‘ma’’.)
Office hour: TBD.

TAs

Bongjung Sung
Email: firstname DOT lastname AT duke DOT edu (Please replace ‘‘firstname’’ with ‘‘bongjung’’ and ‘‘lastname’’ with ‘‘sung’’.)
Office hours: Mon 4-5pm and Tue 4-5pm (tentative). Location: TBD.

Classes

WF 1:25-2:40PM in Old Chem 025.

Readings

Textbooks

Other references (that may be helpful but are not necessary)

Grading

Homework: Weekly problem sets, due by noon on Wednesdays (15%).

Exams: One midterm (35%) and one cumulative final exam (50%). There will be no make-up exams. If you miss the midterm due to for example short-term illness or unresolvable conflict, the final exam will count for both exams (i.e., 85%).

Late homework policy: Homework turned in after class but on the due day will be counted as one day late. The next day will be two days late, etc. No homework more than three days late will be accepted. Each late day will result in a one-level down-grade of that homeowork. Up to two late days will be forgiven at the end of the semester to allow exceptions such as sickness and unresolvable conflicts.

Academic integrity: 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 University Judicial Board. Additionally, there may be penalties to your final class grade. Please review Duke's Standards of Conduct.