Course: MATH 541A, Graduate Mathematical Statistics, Spring 2022
Prerequisite: 1 from (Math 505A or Math 407 or Math 408). Note: once you complete 541A, you cannot take 505A for credit.
Course Content: Parametric families of distributions, sufficiency. Estimation: methods of moments, maximum likelihood, unbiased estimation. Comparison of estimators, optimality, information inequality, asymptotic efficiency. EM algorithm, jacknife and bootstrap.
Last update: 10 January 2021

Instructor: Steven Heilman, stevenmheilman(@-symbol)
Office Hours: Tuesdays, 9AM-11AM, on zoom [link posted on blackboard]
Lecture Meeting Time/Location: Mondays, Wednesdays and Fridays 11AM-1150AM, THH 114
TA: Maria Allayioti, allayiot(@-symbol)
TA Office Hours: ... (the Math Center)
Recommended Textbook: Cassella and Berger, Statistical Inference, 2nd Edition. 
Other Textbooks (not required): Keener, Theoretical Statistics

Midterm 1: Friday Feb 25, 11AM-1150AM, THH 114
Midterm 2: Wednesday Apr 6, 11AM-1150AM, THH 114
Final Exam: Wednesday May 4, 11AM-1PM, THH 114
Other Resources: An introduction to mathematical arguments, Michael Hutchings, An Introduction to Proofs, How to Write Mathematical Arguments
Email Policy:

Exam Procedures: Students must bring their USCID cards to the midterms and to the final exam. Phones must be turned off. Cheating on an exam results in a score of zero on that exam. Exams can be regraded at most 15 days after the date of the exam. This policy extends to homeworks as well. All students are expected to be familiar with the USC Student Conduct Code. (See also here.)
Accessibility Services: If you are registered with accessibility services, I would be happy to discuss this at the beginning of the course. Any student requesting accommodations based on a disability is required to register with Accessibility Services (OSAS) each semester. A letter of verification for approved accommodations can be obtained from OSAS. Please be sure the letter is delivered to me as early in the semester as possible. OSAS is located in 301 STU and is open 8:30am-5:00pm, Monday through Friday.
213-740-0776 (phone)
213-740-6948 (TDD only)
213-740-8216 (fax)

Discrimination, sexual assault, and harassment are not tolerated by the university. You are encouraged to report any incidents to the Office of Equity and Diversity or to the Department of Public Safety This is important for the safety whole USC community. Another member of the university community - such as a friend, classmate, advisor, or faculty member - can help initiate the report, or can initiate the report on behalf of another person. The Center for Women and Men provides 24/7 confidential support, and the sexual assault resource center webpage describes reporting options and other resources.

Exam Resources: Here is a page containing USC Stats A Qual Exams with solutions. Here are exams from the last time I taught this class: Exam 1 Exam 1 Solution Exam 2 Exam 2 Solution Final Final Solution .

Homework Policy:

Grading Policy:

Tentative Schedule: (This schedule may change slightly during the course.)

Week Monday Tuesday Wednesday Thursday Friday
1 Jan 10: 1.1-1.6, Review of Probability Jan 12: 1.1-1.6, Review of Probability Jan 14: 2.1-2.4, Review of Probability
2 Jan 17: No class (MLK Day) Jan 19: 2.1-2.4, Review of Probability Jan 21: Homework 1 due. 3.1-3.6, Review of Probability
3 Jan 24: 3.4, Exponential Families Jan 26: 3.4, Exponential Families Jan 28: 4.1-4.7, Review of Probability
4 Jan 31: 4.1-4.7, Review of Probability Feb 2: 4.1-4.7, Review of Probability Feb 4: Homework 2 due. 5.1 Random Sample
5 Feb 7: 5.2, Sums of Random Variables Feb 9: 5.3, Sampling from the Normal Feb 11: 5.4, Order Statistics
6 Feb 14: 5.4, Order Statistics Feb 16: 5.5, Modes of Convergence Feb 18: Homework 3 due. 5.5, Delta Method
7 Feb 21: No class Feb 23: 5.6, Generating a Random Sample Feb 25: Midterm 1
8 Feb 28: 5.6, Generating a Random Sample Mar 2: 6.2, Sufficiency Mar 4: 6.2, Sufficiency
9 Mar 7: 6.2.4, Completeness Mar 9: 6.3, Likelihood Mar 11: Homework 4 due. 6.4, Equivariance
10 Mar 14: No class (spring break) Mar 16: No class (spring break) Mar 18: No class (spring break)
11 Mar 21: 7.2, Point Estimation Mar 23: 7.2.1, Method of Moments Mar 25: Homework 5 due. 7.2.2, Maximum Likelihood Estimators
12 Mar 28: 7.2.2, Maximum Likelihood Estimators Mar 30: 7.2.2, Maximum Likelihood Estimators Apr 1: 7.2.3, Bayes Estimator
13 Apr 4: 7.2.4, EM Algorithm Apr 6: Midterm 2 Apr 8: 7.3, Comparison of Estimators
14 Apr 11: 7.3.2, Unbiased Estimators Apr 13: 7.3.2, Unbiased Estimators Apr 15: Homework 6 due. 7.3.3, Sufficiency and Unbiasedness
15 Apr 18: 7.3.3, Sufficiency and Unbiasedness Apr 20: 7.3.4, Loss Function Optimality Apr 23: 7.3.4, Loss Function Optimality
16 Apr 25: 7.66, Jackknife Resampling Apr 27: 10.1.4, Bootstrapping Apr 29: Homework 7 due. Review of course (last day of class)

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Homework .tex files

Exam Solutions

Supplementary Notes