Welcome to CSI 973 / STAT 973

Mathematical Statistics II

Spring, 2010

Instructor: James Gentle

Lectures: Tuesday, 4:30-7:10pm, Research I 301.

Some of the lectures will be based on the instructor's notes posted on this website. Some lectures will be accompanied only by notes written on the board.

If you send email to the instructor, please put "CSI 973" or "STAT 973" in the subject line.

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 (25)
  • a midterm consisting of an in-class component and, possibly, a take-home component (35)
  • a final exam consisting of an in-class component and, possibly, a take-home component (40)

    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 long 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.

    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.
    Notes are posted in a password-protected directory.
    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", especially those marked with an asterisk.

    Week 1, January 19

    Brief survey of material covered in 972.
    Review of statistical methods based on likelihood.
    Reading assignment: Companion notes, Chapter 5.
    Exercises for practice and discussion: In Shao: problems 4.96(a)(g)(h), 4.107, 4.151, 5.20, 5.21
    Assignment 1, due January 26: In Shao: problems 3.44, 3.52, 3.91, 3.109, 3.114, 4.94, 4.95, 4.97, 4.109, 4.120, 4.152, 5.90.
    This is a long assignment. It is an assignment from 972 in the fall, but it was not collected, and we did not discuss it.

    Week 2, January 26

    Likelihood methods.

    Week 3, February 2

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

    Week 4, February 9

    Statistical hypothesis testing.
    Class canceled due to snow.
    Read Shao Chapter 6 and Companion Chapter 6.
    Note the new date for the final exam.

    The schedule for the remainder of the semester has been adjusted only slightly. I want the midterm to be before the spring break as originally scheduled; therefore, the midterm may not cover hypothesis testing to the extent that I had originally planned.
    The topic for the new date for Week 14 (May 4) is currently listed as "Review". The specifics will depend on what adjustments I make to other topics as the semester progresses.

    Exercises for practice and discussion: In Shao: problems 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 2: In Shao: problems 6.1, 6.5(a),(b)(c), 6.12, 6.21, 6.23, 6.27(a)(b)(c)
    due February 23

    Week 4, February 16

    Statistical hypothesis testing.
    Assignment 3, due February 23: In Shao: problems 6.38, 6.52(a)(b), 6.92(a)(b), 6.99(a)(b)

    Week 5, February 23

    Statistical hypothesis testing.

    Week 6, March 2

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

    Week 7, March 16 (Class does not meet March 9)

    Confidence sets
    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 4, due March 23: 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 8, March 23

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

    Week 9, March 30

    Equivariant methods

    Week 10, April 6

    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 6, due April 20: In Shao: problems 5.3, 5.9, 5.24, 5.27, 5.39, 5.96

    Week 11, April 13

    Robust methods

    Week 12, April 20

    Function estimation
    Exercises for practice and discussion: In Shao: problems 5.15, 5.16, 5.17, 5.23 (Solutions in Shao, 2005)
    Assignment 7, due April 27: In Shao: problems 5.18, 5.19

    Week 13, April 27

    Probability density function estimation

    Week 14, May 4


    Saturday May 8 4:30-6:30pm
    Final Exam

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