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Mathematical Statistics II
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.
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
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Mathematical Statistics II
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 24
Brief survey of material covered in 972.
Unbiased estimation. Reading assignment: Reread/review Shao, Chapter 3, Companion, Chapter 4.
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