Course: MATH 541A, Graduate Mathematical Statistics, Spring 2023
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: 27 October 2022

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: Cora Liang, ziyilian(@-symbol)
TA Office Hours: (see the schedule in the Math Center)
Recommended Textbook: Cassella and Berger, Statistical Inference, 2nd Edition. 
Other Textbooks (not required): Keener, Theoretical Statistics

Midterm 1: Friday Feb 24, 11AM-1150AM, THH 114
Midterm 2: Wednesday Apr 5, 11AM-1150AM, THH 114
Final Exam: Wednesday, May 3, 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)

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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 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 9: 1.1-1.6, Review of Probability Jan 11: 1.1-1.6, Review of Probability Jan 13: 2.1-2.4, Review of Probability
2 Jan 16: No class (MLK Day) Jan 18: 2.1-2.4, Review of Probability Jan 20: Homework 1 due. 3.1-3.6, Review of Probability
3 Jan 21: 3.4, Exponential Families Jan 25: 3.4, Exponential Families Jan 27: 4.1-4.7, Review of Probability
4 Jan 30: 4.1-4.7, Review of Probability Feb 1: 4.1-4.7, Review of Probability Feb 3: Homework 2 due. 5.1 Random Sample
5 Feb 6: 5.2, Sums of Random Variables Feb 8: 5.3, Sampling from the Normal Feb 10: 5.4, Order Statistics
6 Feb 13: 5.4, Order Statistics Feb 15: 5.5, Modes of Convergence Feb 17: Homework 3 due. 5.5, Delta Method
7 Feb 20: No class Feb 22: 5.6, Generating a Random Sample Feb 24: Midterm 1
8 Feb 27: 5.6, Generating a Random Sample Mar 1: 6.2, Sufficiency Mar 3: 6.2, Sufficiency
9 Mar 6: 6.2.4, Completeness Mar 8: 6.3, Likelihood Mar 10: Homework 4 due. 6.4, Equivariance
10 Mar 13: No class (spring break) Mar 15: No class (spring break) Mar 17: No class (spring break)
11 Mar 20: 7.2, Point Estimation Mar 22: 7.2.1, Method of Moments Mar 24: Homework 5 due. 7.2.2, Maximum Likelihood Estimators
12 Mar 27: 7.2.2, Maximum Likelihood Estimators Mar 29: 7.2.2, Maximum Likelihood Estimators Mar 30: 7.2.3, Bayes Estimator
13 Apr 3: 7.2.4, EM Algorithm Apr 5: Midterm 2 Apr 7: 7.3, Comparison of Estimators
14 Apr 10: 7.3.2, Unbiased Estimators Apr 12: 7.3.2, Unbiased Estimators Apr 14: Homework 6 due. 7.3.3, Sufficiency and Unbiasedness
15 Apr 17: 7.3.3, Sufficiency and Unbiasedness Apr 19: 7.3.4, Loss Function Optimality Apr 22: 7.3.4, Loss Function Optimality
16 Apr 24: 7.66, Jackknife Resampling Apr 26: 10.1.4, Bootstrapping Apr 28: Homework 7 due. Review of course (last day of class)

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Homework .tex files

Exam Solutions

Supplementary Notes