Welcome to CSI 973 / STAT 973

Mathematical Statistics II

Spring, 2011

Instructor: James Gentle

Lectures: Tuesday, 4:30-7:10pm, Nguyen Engineering Building 1107.

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.

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. My assigned "exercises for practice and discussion" are all solved (or at least partially solved) in this book.
I will also use my Companion notes.
See also the references listed in the general description.

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.

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

  • homework assignments (20)
  • 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. 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).
    Students are strongly encouraged to solve the "exercises for practice and discussion".

    Week 1, January 25

    Brief survey of material covered in 972.
    Unbiased estimation. Reading assignment: Reread/review Shao, Chapter 3.
    Assignment 1, due February 8: In Shao: problems 3.44, 3.52, 3.60, 3.91, 3.106, 3.107, 3.109, 3.111, 3.114, 4.67, 4.68, 4.71, 4.72
    This is a long assignment, but much of it is an assignment from 972 in the fall that was not collected or discussed.

    Week 2, February 1

    Likelihood methods.

    Exercises for practice and discussion: In Shao: problems 4.96(all)), 4.107, 4.151 (Solutions in Shao, 2005) Assignment 2, due February 15: In Shao: problems 4.94, 4.95, 4.96 (a)(g)(h)(i), 4.97, 4.109, 4.120, 4.140, 4.152

    Week 3, February 8

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

    Week 4, February 15

    Some follow-up from last week.
    Statistical hypothesis testing; intro.

    Exercises for practice and discussion: In Shao: problems 5.20, 5.21 6.2, 6.3, 6.4, 6.6, 6.10, 6.17, 6.20, 6.29, 6.37, 6.51, 6.52, 6.58, 6.93, 6.98, 6.123 (Solutions in Shao, 2005)
    Assignment 3, due February 22: In Shao: problems 6.1, 6.5(a),(b)(c), 6.12, 6.21, 6.23, 6.27(a)(b)(c)

    Week 5, February 22

    Statistical hypothesis testing.
    Assignment 4, due March 1: In Shao: problems 6.28, 6.38(a), 6.52(a)(b), 6.92(a)(b), 6.99(a)(b)

    Week 6, March 1

    Statistical hypothesis testing.

    Week 7, March 8

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

    Week 8, March 22 (Class does not meet March 15)

    Some more on tests
    Confidence sets
    Equivariant methods

    Exercises for practice and discussion: In Shao: problems 7.9, 7.18, 7.29, 7.31, 7.48, 7.60, 7.63, 7.67 (Solutions in Shao, 2005)
    Assignment 5, due March 29: In Shao: problems 7.1, 7.2, 7.22(a), 7.22(b), 7.44, 7.79, 7.82, 7.93, 7.95, 7.101

    Week 9, March 29

    Equivariant methods
    Exercises for practice and discussion: In Shao: problems 4.47, 4.52 (Solutions in Shao, 2005)
    Assignment 6, due April 5: In Shao: problems 4.57(a), 6.63, 6.69(a), 6.72, 6.74, 7.58, 7.59

    Week 10, April 5

    Robust methods
    Exercises for practice and discussion: In Shao: problems 5.5, 5.59, 5.61, 5.63, 5.74, 5.86, 5.111 (Solutions in Shao, 2005)
    Assignment 7, due April 19: In Shao: problems 5.3, 5.9, 5.24, 5.27, 5.39, 5.96

    Week 11, April 12

    Robust methods

    Week 12, April 19

    Function estimation
    Exercises for practice and discussion: In Shao: problems 5.15, 5.16, 5.17, 5.23 (Solutions in Shao, 2005)
    Assignment 8, due April 26: In Shao: problems 5.18, 5.19

    Week 13, April 26

    Probability density function estimation

    Week 14, May 3

    Other topics; review
    Lecture Notes:
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    May 17 4:30-7:15pm
    Final Exam

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