Welcome to CSI 973 / STAT 973

Mathematical Statistics II

Spring, 2013

Instructor: James Gentle

Lectures: Tuesday, 4:30-7:10pm, Engineering Building 4457.

This course is part of a two-course sequence. The general description of the two courses is available at mason.gmu.edu/~jgentle/csi9723/

The prerequisites for this course include CSI 972 / STAT 972.

This course is a continuation of CSI 972 / STAT 972. It covers various topics in statistical inference, including procedures based on likelihood, principles of testing and formation of confidence sets, equivariant statistical procedures, nonparametric and robust procedures, and nonparametric density estimation.

One learns mathematical theory primarily by individual work; that is, by supplying the successive steps in solving a problem or proving a theorem. Some mathematical theory is learned and reinforced by passive activities such as reading or listening to lectures and discussions, and the assigned readings and weekly lectures are meant to serve this purpose. The reading assignments listed in the schedule below should be carried out with a pencil and paper in hand. The readings should be iterated as necessary to achieve a complete understanding of the material.

Students in this course are likely in the last stages of their coursework for a PhD in statistics or a related field. Such students should participate in the scholarly activities of the field, including attending seminars and conferences, reading the literature, and contributing to the literature. Many of these activities are coordinated through professional or learned societies, such as the American Statistical Association (ASA) and the Institute of Mathematical Statistics (IMS).

ASA offers membership to students for $15 annually and IMS offers free memberships for full-time students. You should join one or both. Membership provides online access to journals.

You should also be familiar with various ways of accessing the statistical literature. The GMU Library provides access through JSTOR and Project Euclid.


The text is Jun Shao (2003), Mathematical Statistics, second edition, Springer.
Be sure to get the corrections at the author's website
A useful supplement is Jun Shao (2005), Mathematical Statistics: Exercises and Solutions, Springer.
I will also use my Companion notes.
See also the references listed in the general description.

While this course is a continuation of CSI972/STAT972, the textbook for this course is not a continuation of the text used in CSI972/STAT972. That text and generally the material covered in CSI972/STAT972 addressed point estimation specifically. The first two chapters of the text for this course integrates point estimation with other types of statistical inference. The next three chapters of Shao are on point estimation, but they cover several topics that were not covered in CSI972/STAT972. The final two chapters of Shao are on hypothesis testing and confidence sets.

The general plan for this course will be to cover several topics in point estimation that were not covered in CSI972/STAT972, and then to cover hypothesis testing and confidence sets.

Student work in the course (and the relative weighting of this work in the overall grade) will consist of

  • homework assignments (20)
  • a written report (5 to 10 pages) and an in-class presentation about a research article in the recent statistical literature (15)
  • a midterm consisting of an in-class component and, possibly, a take-home component (30)
  • a final exam (in-class) (35)

    Each homework will be graded based on 100 points, and 5 points will be deducted for each day that the homework is late. The homework assignments are long, so they should be begun well before they are due. Start each problem on a new sheet of paper and label it clearly. The problems do not need to be worked sequentially (some are much harder than others); when you are stuck on one problem, go on to the next one.

    For the in-class presentation, students will be allowed to choose an article from a list from recent issues of Annals of Statistics. The presentation will be 30 to 45 minutes and will summarize the main results of the article, providing derivations and proofs as appropriate. The publisher, the Institute of Mathematical Statistics (IMS), makes the content of Annals of Statistics available through Project Euclid. Slightly older issues are available through JSTOR.

    The issues can be accessed through the GMU Library portal http://library.gmu.edu/ by going to E-Journals, and entering the name of the journal. After that, you select Project Euclid, at which point you must enter your GMU email username and password. (You may get a security message asking that you allow MathPlayer to run. It's OK to allow it.)

    Each student enrolled in this course must assume the responsibilities of an active participant in GMU's scholarly community in which everyone's academic work and behavior are held to the highest standards of honesty. The GMU policy on academic conduct will be followed in this course.

    Except during a period in which a take-home exam is being worked on, students are free to discuss homework problems or other topics with each other or anyone else, and are free to use any reference sources. Group work and discussion outside of class is encouraged, but of course explicit copying of homework solutions should not be done.

    Students are not to communicate concerning exams with each other or with any person other than the instructor. On take-home exams, any passive reference is permissible (that is, the student cannot ask someone for information, but the student may use any existing information from whatever source).

    For in-class exams, one sheet of notes will be allowed. The preparation of that sheet is one of the most important learning activities.

    An approximate schedule is shown below. As the semester progresses, more details may be provided, and there may be some slight adjustments.
    Students are expected to read the relevant material in the text prior to each class (after the first one).


    Week 1, January 22

    More on unbiased estimation (Shao, Chapter 3):
    Estimation in linear models
    Estimation in sample surveys
    Asymptotic unbiasedness

    Reading assignment: Shao, Chapter 4, Companion, Chapter 6.
    Assignment 1, due January 29: In Shao: problems 3.44 (typo: should be nU_n), 3.48, 3.52, 3.53, 3.60, 3.90, 3.91, 3.107 (typo: should be alpha/beta), 3.111

    Week 2, January 29

    Discuss project
    Likelihood methods.

    Project Assignment, due February 5: Full bibliographic information on two articles from Annals of Statistics, and for each a brief description. The articles must each be 5 pages or longer. Your description should be about a page.
    Do not just copy from the abstract. Do not plagiarize.
    Assignment 2, due February 5: In Shao: problems 4.94, 4.95, 4.96(b)(c)(g)(h), 4.97, 4.106

    Week 3, February 5

    Likelihood methods.
    Assignment 3, due February 12: In Shao: problems 4.109, 4.120, 4.125, 4.126(b)(c)(g)(h), 4.140

    Week 4, February 12

    More on likelihood methods.
    Generalized estimating equations.
    Asymptotic properties.
    Variations on likelihood methods.
    Project Assignment, due February 26: Select one article from Annals of Statistics, possibly one of the two from the previous assignment, and write a more complete description (2 or 3 pages). You should make this description clear and readable. Your description should be well-organized, and your sentences should be complete and grammatically correct.
    Assignment 4, due February 19: In Shao: problems 4.146, 4.147, 4.149, 4.150(a)(b), 4.152

    Week 5, February 19

    Statistical hypothesis testing.

    Week 6, February 26

    Statistical hypothesis testing.

    Week 7, March 5

    Midterm exam. Closed book, closed notes, and closed computers except for one sheet (front and back) of prewritten notes.

    Week 8, March 19 (Class does not meet March 12)

    More on tests: similar regions; types of tests; Bayes testing.
    Assignment 6, due March 26: In Shao: problems 6.100, 6.104, 6.106, 6.107, 6.109, 6.111, 6.112, 6.114, 6.122

    Week 9, March 26

    More on tests: similar regions; types of tests; Bayes testing.
    Assignment 7, due April 2: In Shao: problems 6.28, 6.38(a), 6.52(a)(b), 6.63, 6.69(a), 6.72, 6.74(a), 6.92(a)(b), 6.99(a)(b)
    I had intended for some of the problems on this list to have been assigned earlier, however, I had inadvertently misplaced some of the HTML comment directives.

    Week 10, April 2

    Confidence sets
    Equivariant methods
    Bayesian methods in testing and confidence regions
    Assignment 8, due April 16: In Shao: problems 7.1, 7.2, 7.22(a), 7.22(b), 7.44, 7.58, 7.59, 7.79, 7.82, 7.93(a), 7.93(b), 7.95(a), 7.101

    Week 11, April 9

    Robust methods

    Week 12, April 16

    Robust methods and functional calculus
    Projects due Presentations by 2 randomly selected students.
    Assignment 9 (will not be turned in): In Shao: problems 5.3, 5.9, 5.18, 5.19, 5.24

    Week 13, April 23

    Robust methods and function estimation
    Presentations by remaining students.

    Week 14, April 30

    Other topics; review

    May 14 4:30-7:15pm
    Final Exam

    Closed book and closed notes except for one sheet of prewritten notes.