Washington University in St. Louis · Fall 2026

SDS 4020 Mathematical Statistics

Provisional weekly schedule and course materials

Instructor: Likai Chen · likai.chen@wustl.edu

Return to syllabus

Class meetings: Tue/Thu 11:30 a.m.–12:50 p.m. in MCMILLAN 0G052. Midterm: Tuesday, October 13. Thursday, October 8 is an independent review day with no in-person class. Topic pacing may be adjusted during the semester.

Fall 2026 course plan
Week Class dates Topics and milestones Textbook sections Lecture notes
1 · Aug 24–28 Tue Aug 25Thu Aug 27 Course orientation; review of moment-generating functions; special distributions and relationships among them. Review; §§3.5–3.6 1. Special Distributions
2 · Aug 31–Sep 4 Tue Sep 1Thu Sep 3 Special and sampling distributions; transformation ideas; introduction to statistical inference and point estimation. §§3.5–3.6; §4.1 1. Special Distributions
2. Introduction to Statistical Inference
3 · Sep 7–11 Tue Sep 8Thu Sep 10 Bias, variance, mean squared error, consistency, and introductory confidence intervals. §§4.1–4.2 2. Introduction to Statistical Inference
4 · Sep 14–18 Tue Sep 15Thu Sep 17 Confidence intervals and pivots; hypothesis-testing framework; Z, t, and F procedures. §4.2; §§4.5–4.6 2. Introduction to Statistical Inference
5 · Sep 21–25 Tue Sep 22Thu Sep 24 Chi-square testing; order statistics and their distributions. §4.7; §§4.4, 4.8 3. Chi-square Tests
4. Order Statistics
6 · Sep 28–Oct 2 Tue Sep 29Thu Oct 1 Order statistics continued; synthesis of pre-midterm material. §§4.4–4.8 4. Order Statistics
7 · Oct 5–9 Tue Oct 6 · Fall BreakThu Oct 8 · Independent review; no in-person class Fall Break Oct 3–6
Students use the posted review materials to prepare independently for the midterm.
Pre-midterm material Review materials distributed in Canvas
8 · Oct 12–16 Tue Oct 13 · MidtermThu Oct 15 Midterm Tuesday, 11:30 a.m.–12:50 p.m., MCMILLAN 0G052.
Modes of convergence and asymptotic reasoning begin Thursday.
Pre-midterm material; §5.1 5. Convergence
9 · Oct 19–23 Tue Oct 20Thu Oct 22 Modes of convergence, laws of large numbers, and the central limit theorem; likelihood functions and maximum-likelihood estimators. §§5.1–5.3; §6.1 5. Convergence
6. Likelihood Function and MLE Properties
10 · Oct 26–30 Tue Oct 27Thu Oct 29 Fisher information; Cramér–Rao lower bound and efficiency. §6.2 7. Fisher Information
8. Cramér–Rao Theory
11 · Nov 2–6 Tue Nov 3Thu Nov 5 Cramér–Rao theory continued; likelihood-ratio tests. §§6.2–6.4 8. Cramér–Rao Theory
9. Likelihood-ratio Tests
12 · Nov 9–13 Tue Nov 10Thu Nov 12 Likelihood-ratio methods and general testing; introduction to sufficient statistics. §§6.3–6.4; §7.2 9. Likelihood-ratio Tests
10. Sufficiency
13 · Nov 16–20 Tue Nov 17Thu Nov 19 Sufficiency and the factorization theorem; complete families and their consequences. §§7.2–7.7 10. Sufficiency
11. Completeness I
14 · Nov 23–27 Tue Nov 24Thu Nov 26 · Thanksgiving Break Completeness continued. Thanksgiving Break Nov 25–29 §§7.4–7.7 11. Completeness I
12. Completeness II
15 · Nov 30–Dec 4 Tue Dec 1Thu Dec 3 · Last SDS 4020 meeting UMVUE and Lehmann–Scheffé ideas; Neyman–Pearson lemma and uniformly most powerful tests; final review as time permits. §§7.1, 7.3; §§8.1–8.3 12. Completeness II
13. UMP Tests
Finals · Dec 10–16 Exact date, time, and location assigned by the university Cumulative final examination Cumulative Practice materials distributed in Canvas

Calendar anchors: first day of classes August 24; Labor Day September 7; Fall Break October 3–6; Thanksgiving Break November 25–29; last day of classes December 7; reading days December 8–9; final exams December 10–16.