Welcome to CSI 973 / STAT 973

Mathematical Statistics II

Spring, 2012

Instructor: James Gentle

Lectures: Tuesday, 4:30-7:10pm, Innovation Hall 209.

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.

Syllabus

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.

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 consisting of an in-class component and, possibly, a take-home component (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).

    Schedule

    Week 1, January 24

    Brief survey of material covered in 972.
    Unbiased estimation; discussion of some exercises in the last assignments of 972: in Shao problems, 3.9, 3.15, 3.32(a)(c)(g), 3.35(a)(b)(c), 3.43, 3.45, 3.46, 3.61.
    Reading assignment: Reread/review Shao, Chapter 3, Companion, Chapter 4.
    Assignment 1, due January 31: In Shao: problems 3.44, 3.52, 3.60, 3.91, 3.106, 3.107, 3.109, 3.111, 3.114

    Week 2, January 31

    Likelihood methods.

    Assignment 2, due February 14: In Shao: problems , 4.67 4.68, 4.71, 4.72, 4.94, 4.95, 4.96(b)(c)(g)(h), 4.97, 4.109, 4.120, 4.140, 4.152
    Project Assignment, due February 14: Full bibliographic information on two articles from Annals of Statistics, and for each a brief description.
    Do not just copy from the abstract. Do not plagiarize.

    Week 3, February 7

    Likelihood methods.

    Week 4, February 14

    More on likelihood methods.
    Generalized estimating equations.
    Asymptotic properties.
    Variations on likelihood methods.

    Assignment 3, due February 21: In Shao: problems 4.106, 4.125, 4.126(b)(c)(g)(h), 4.147, 4.149

    Week 5, February 21

    Statistical hypothesis testing.
    Assignment 4, due February 28: In Shao: problems 6.28, 6.38(a), 6.52(a)(b), 6.92(a)(b), 6.99(a)(b)

    Week 6, February 28

    Statistical hypothesis testing.

    Week 7, March 6

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

    Week 8, March 20 (Class does not meet March 13)

    Some more on tests
    Assignment 5, due March 27: In Shao: problems 6.100, 6.104, 6.109, 6.111, 6.112, 6.114, 6.122

    Week 9, March 27

    Confidence sets
    Equivariant methods
    Assignment 6, due April 10: In Shao: problems 4.57(a), 6.63, 6.69(a), 6.72, 6.74(a), 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 10, April 3

    Equivariant methods
    Robust methods

    Week 11, April 10

    Robust methods
    Assignment 7, due April 17: In Shao: problems 5.3, 5.9, 5.18, 5.19, 5.24

    Week 12, April 17

    Function estimation
    Projects due Presentations by 3 randomly selected students.
    Assignment 8, due April 24: In Shao: problems 5.27, 5.45, 5.47(a)(c), 5.96

    Week 13, April 24

    Probability density function estimation
    Presentations by remaining students.

    Week 14, May 1

    Other topics; review

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

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