Course: MATH 541A, Graduate Mathematical Statistics, Spring 2019
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: 28 February 2019
Instructor: Steven Heilman, stevenmheilman(@-symbol)gmail.com
Office Hours: Mondays, 9AM-11AM, Wednesdays 10AM-11AM, or by appointment, KAP 406G
Lecture Meeting Time/Location: Mondays, Wednesdays and Fridays 11AM-1150AM, THH 114
TA: Man Luo, manl(@-symbol)usc.edu
TA Office Hours: Mondays 5PM-6PM, Thursdays 10AM-12PM, KAP 263 (the Math Center)
Recommended Textbook: Cassella and Berger, Statistical Inference, 2nd Edition. (A link is available here).
Other Textbooks (not required): Keener, Theoretical Statistics. (A link is available here).
Midterm 1: Feb 22, 11AM-1150AM, THH 114
Midterm 2: Apr 3, 11AM-1150AM, THH 114
Final Exam: May 1, 11AM-1PM, Location TBD
Other Resources: An introduction to mathematical arguments, Michael Hutchings, An Introduction to Proofs, How to Write Mathematical Arguments
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.)
Disability Services: If you are registered with disability 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 Disability Services and Programs (DSP) each semester. A letter of verification for approved accommodations can be obtained from DSP. Please be sure the letter is delivered to me as early in the semester as possible. DSP is located in 301 STU and is open 8:30am-5:00pm, Monday through Friday.
213-740-6948 (TDD only)
Exam Resources: Here is a page containing USC Stats A Qual Exams with solutions. Here and here are former 541A course pages with several helpful links and references.
Tentative Schedule: (This schedule may change slightly during the course.)
|1||Jan 7: 1.1-1.6, Review of Probability||Jan 9: 1.1-1.6, Review of Probability||Jan 11: 2.1-2.4, Review of Probability|
|2||Jan 14: 2.1-2.4, Review of Probability||Jan 16: 3.1-3.6, Review of Probability||Jan 18: Homework 1 due. 3.4, Exponential Families|
|3||Jan 21: No class (MLK Day)||Jan 23: 3.4, Exponential Families||Jan 25: 4.1-4.7, Review of Probability|
|4||Jan 28: 4.1-4.7, Review of Probability||Jan 30: 4.1-4.7, Review of Probability||Feb 1: Homework 2 due. 5.1 Random Sample|
|5||Feb 4: 5.2, Sums of Random Variables||Feb 6: 5.3, Sampling from the Normal||Feb 8: 5.4, Order Statistics|
|6||Feb 11: 5.4, Order Statistics||Feb 13: 5.5, Modes of Convergence||Feb 15: Homework 3 due. 5.5, Delta Method|
|7||Feb 18: No class||Feb 20: 5.6, Generating a Random Sample||Feb 22: Midterm 1|
|8||Feb 25: 5.6, Generating a Random Sample||Feb 27: 6.2, Sufficiency||Mar 1: 6.2, Sufficiency|
|9||Mar 4: 6.2.4, Completeness||Mar 6: 6.3, Likelihood||Mar 8: Homework 4 due. 6.4, Equivariance|
|10||Mar 11: No class (spring break)||Mar 13: No class (spring break)||Mar 15: No class (spring break)|
|11||Mar 18: 7.2, Point Estimation||Mar 20: 7.2.1, Method of Moments||Mar 22: Homework 5 due. 7.2.2, Maximum Likelihood Estimators|
|12||Mar 25: 7.2.2, Maximum Likelihood Estimators||Mar 27: 7.2.2, Maximum Likelihood Estimators||Mar 29: 7.2.3, Bayes Estimator|
|13||Apr 1: 7.2.4, EM Algorithm||Apr 3: Midterm 2||Apr 5: 7.3, Comparison of Estimators|
|14||Apr 8: 7.3.2, Unbiased Estimators||Apr 10: 7.3.2, Unbiased Estimators||Apr 12: Homework 6 due. 7.3.3, Sufficiency and Unbiasedness|
|15||Apr 15: 7.3.3, Sufficiency and Unbiasedness||Apr 17: 7.3.4, Loss Function Optimality||Apr 19: 7.3.4, Loss Function Optimality|
|16||Apr 22: 7.66, Jackknife Resampling||Apr 24: 10.1.4, Bootstrapping||Apr 26: Homework 7 due. Review of course (last day of class)|
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Homework .tex files