Updated October 19, 2026. This webpage is the authoritative course syllabus; the Word document is a dated snapshot. Policy changes are announced on Canvas. Canvas holds assignment deadlines, submissions, and grades.
Course information
- Lectures
- Mondays & Wednesdays, 11:00 a.m.–12:15 p.m.
Van Vleck B211 - Weekly work
- Two 75-minute lectures, one discussion section, assigned readings, and homework.
- Discussion
- Fridays, 11:00 a.m.–12:15 p.m.,
2533 Morgridge Hall - Enrollment
- See the current UW Guide requisites below.
Yiqiao (Joe) Zhong
Office hour
Mondays, 12:30–1:30 p.m.
5655 Morgridge Hall
Fuxin Wang
Office hour
Fridays, 1:00–2:00 p.m.
2517 Morgridge Hall
About the course
STAT 709 is a core course in the Statistics Ph.D. curriculum and the first course in the mathematical statistics sequence, followed by STAT 710. It introduces the foundations of statistical theory and prepares doctoral students to read, evaluate, and conduct theoretical statistical research.
Learning outcomes
By the end of the course, you should be able to:
- Formulate statistical estimation problems using rigorous mathematical language.
- Derive fundamental properties of estimators, including bias and variance.
- Compare estimators and explain the strengths and limitations of competing methods.
- Apply theoretical tools, including concentration inequalities, to new statistical problems and present the resulting arguments as mathematical proofs.
- Distinguish classical large-sample theory from high-dimensional statistical theory and critically evaluate recent research.
Credits and expected work
STAT 709 is a 4-credit, in-person course. We meet for two 75-minute lectures and one 75-minute discussion each week. Plan for about 8 hours of reading, homework, and study outside class each week, with approximately 180 hours of total engagement over the semester. This follows UW’s 45-hours-per-credit standard.
Regular and substantive interaction: weekly lectures and discussion, weekly instructor and TA office hours, written homework feedback, and Canvas Discussions.
Course designation and enrollment
The UW Guide lists STAT/MATH 709 as Mathematical Statistics I, with the designation “Grad 50% — Counts toward 50% graduate coursework requirement.” The course is not repeatable for credit.
For enrollment, the Guide lists the Statistics MS or Ph.D., Biomedical Data Science MS or Ph.D., and the Statistics doctoral minor. Consult the current Guide entry for official requisites.
Grading
| Component | Points | Weight |
|---|---|---|
| Class participation | 20 | 20% |
| Homework assignments | 20 | 20% |
| Midterm examination | 20 | 20% |
| Final examination | 40 | 40% |
| Total | 100 | 100% |
Bonus points. Details, if any, are to be determined.
Letter grades
Final letter grades will be determined in light of the class’s overall performance. The official UW–Madison Canvas Grading Schemes page explains how numerical scores are converted into letter grades.
The percentages on that page are examples or pre-built Canvas settings, not university-mandated cutoffs. They should not be read as the grading thresholds for STAT 709.
Homework
Download the posted assignments. Follow the AI policy and collaboration rules for every submission.
Weekly assignments provide practice with the definitions, calculations, and proofs developed in class. Problems will come from several sources, including Jun Shao’s Mathematical Statistics, second edition.
- Posting and deadlines. Homework will normally be posted by Sunday evening and due approximately one week later. Consult Canvas for each assignment’s exact deadline.
- Submission. Submit all work through Canvas. LaTeX and legible handwritten solutions are both acceptable.
Late submissions
A 20% deduction applies to work submitted after the deadline but before solutions are posted. Work submitted after solutions are posted receives no credit.
Examinations
Midterm
- Date
- October 14, 2026 · In class
- Duration
- 75 minutes
- Location
- Van Vleck B211
Final examination
- Date
- To be announced
- Duration
- 2 hours
- Location
- To be announced
Notes and calculators. For each exam, you may bring up to two double-sided A4-sized sheets of notes. No AI, calculators, or other electronic aids are permitted, except as provided by an approved accommodation.
Exam scope in the lecture notes. High- and mid-priority material is in scope for examinations, except where a lecture explicitly states an exam exemption. Low-priority material will not be examined; further reading is optional exploration. See the preface’s priority guide for details.
Communication
- Office hours. The instructor and teaching assistant hold office hours each week. See the course information above for the current details.
- General course questions. Use the Canvas Discussions area. You may post anonymously where that option is enabled.
- Urgent or private matters. Email the instructor or teaching assistant, including when illness affects your coursework.
Sign in to UW–Madison Canvas for assignment submissions and course discussions.
Comments on the public lecture pages are visible to everyone. Use Canvas or email for private course matters.
Generative AI in STAT 709
The goal of this course is that you can build and check mathematical arguments yourself. AI can restate a definition, check algebra, suggest a counterexample, or critique a draft proof. It can also do the struggling for you, and that struggle is where understanding develops. Use it to support your learning.
These rules may be refined during the semester. Any change will be announced on Canvas.
AI use on homework
You may use generative AI as a study aid, including entering homework problem statements, unless an assignment says otherwise. Four conditions apply:
- Your solution is your own. Write it yourself, in your own words, and be able to explain every step if asked in office hours or class.
- Disclose your use. End each homework with an “AI use” note giving the tool, the problems, and what you used it for. “No AI used” is fine. Undisclosed use counts as unauthorized assistance.
- Check everything. AI tools can state false results confidently, especially in proofs. You are responsible for every claim you submit.
- Assignment rules take precedence. Follow any problem-specific instructions, including a requirement to work without AI or an invitation to critique an AI-written proof.
Example AI use note. “Copilot, Problem 3: asked for a hint on choosing a dominating function. Problem 5: checked my algebra.”
Exams and presentations
- Exams: no AI or other electronic aids. You may bring up to two double-sided A4 sheets of notes; see the examination rules for calculators and accommodations.
- Participation and presentations: AI may help you prepare. Present in your own words and be ready to answer questions.
Privacy and integrity
Where possible, use UW–Madison’s Microsoft Copilot Chat, signed in with your UW account through NetID. This provides enterprise data protection. Do not enter other students’ work or anyone’s personal information into an AI tool. Follow UW’s current AI data-use guidance.
AI use outside these rules, including undisclosed use, is unauthorized assistance and is subject to UW–Madison’s academic misconduct procedures under UWS 14. I do not use AI-detection software. If I have a concern, I will first ask you to talk through your solution with me.
How AI is used in this course
Lecture notes. The web notes were converted and edited with OpenAI’s Codex, starting from my original lecture notes, which were written without AI and are available under References and resources. I review the content, but conversion can introduce errors. Please report anything that looks wrong.
Assessment. Grades are assigned by the instructor and TA, not by AI.
Collaboration and outside sources
- Discuss homework with classmates, then write your final solutions on your own.
- List the classmates you discussed each problem with.
- Do not share written solutions or copy from solution manuals, previous years’ solutions, or online sources. The Shao exception below permits consultation after your own serious attempt, with citation; it does not permit copying.
- If an idea comes from a book or paper, cite it.
Shao’s solutions book. For problems currently assigned as homework, you may consult solutions after making your own serious attempt. Cite the solutions you consult and write your final solution independently in your own words. Assignment-specific rules take precedence. You may use the book for other practice.
UW policies and student support
Academic integrity
Everyone in this course is expected to uphold UW–Madison’s academic standards. Cheating, fabrication, plagiarism, unauthorized collaboration or AI use, and helping others do these things can lead to disciplinary action. Possible sanctions include a failing assignment or course grade, suspension, or expulsion. See academic misconduct procedures and student rights.
Disability accommodations
Tell me about approved instructional accommodations at the beginning of the semester, or as soon as possible after approval. I will work with you and the McBurney Disability Resource Center to arrange them. Accommodation information is confidential and shared only as needed to implement it. See UW-855.
Religious observances
Notify me within the first two weeks of class, whenever possible, about religious observances that conflict with course requirements so we can arrange an alternative. If a conflict becomes clear later, contact me as soon as possible. See UW-880 and the academic calendar.
Diversity and inclusion
I want students from every background to feel welcome to ask questions, contribute ideas, and learn in this class. Treat one another with respect, including when we disagree. See UW–Madison’s institutional statement on diversity.
Health, well-being, and basic needs
If health concerns, food or housing insecurity, family challenges, or other difficulties affect your coursework, help is available and you are welcome to talk to me. UW’s Get Help guide connects students with support.
Privacy and recordings
- Public notes: you may share the lecture notes made publicly available on this website.
- Private materials: recordings, Canvas-only files, and homework solutions are for your own course use. Do not share, post, or sell them without the instructor’s permission.
- Recording: do not record lectures without the instructor’s permission or an approved accommodation that includes recording. Approved McBurney note-taking arrangements remain allowed.
See the Registrar’s student record privacy information.
Course evaluations
Please complete the confidential course evaluation when invited, typically about two weeks before the semester ends. Your feedback helps improve the course. See UW’s course evaluation information for students.
Rules, rights, and responsibilities
The UW Guide’s rules, rights, and responsibilities section covers student privacy, academic integrity, and grievance routes.
Teaching and learning data
Digital course tools can record access, submissions, and activity. UW’s teaching and learning data transparency statement explains how campus-supported tools collect, use, and protect these data. Follow the privacy guidance above when using AI.
Course outline and readings
The homepage lecture list has the current notes and downloads, organized into seven parts.
- Part I · Foundations: the language of probability — Lectures 1–5.
- Part II · Statistical models and estimators — Lectures 6–8.
- Part III · Large-sample theory — Lectures 9–11.
- Part IV · Optimality — Lectures 12–13.
- Part V · High dimensions: tools and phenomena — Lectures 14–17.
- Part VI · Shrinkage and sparsity — Lectures 18–20 · Optional.
- Part VII · Testing and confidence sets — No lecture entries yet.
Lecture notes are the primary source for many topics. Bickel and Doksum, Mathematical Statistics, Volume I, and Casella and Berger, Statistical Inference, are the principal texts. See References and resources for editions, additional readings, and the original notes.
What changed · October 13, 2026: added AI and collaboration rules, credit expectations, and UW policy links; gathered the full course policies here.