THEORETICAL STATISTICS

This course is intended for PhD students in Statistics, Biostatistics, and other quantitative fields. The prerequisties are:

- A course in mathematical statistics at the level of Stat 512-13
- Probability theory at least at the level of Stat 394-95 (although more will be expected from the students)
- Mathematical analysis at the level of Math 424-426

There is no textbook, although the two-volume set entitled *Breakthroughs in
Statistics edited by Johnson adn Kotz (New York: Springer, 1993)
is recommended.
Jon Wellner's lecture notes from a previous
offering of 581-3 are
available, and are referred to frequently in the
syllabus. Although I will
not lecture from them, they contain much useful material. Dr. Wellner will
be teaching STAT 582-3.
The syllabus contains
references for each section.
(References for Wellner's lecture notes are available separately.)
A variety of books will be on four hour
reserve in the Mathematics-Statistics Research Library.
Part of the purpose
of this is to encourage browsing, and teach you how to find material in
the literature. Furthermore, no single book covers the material we will
be talking about.
There will be lecture notes summaries
(covering what I consider
the most important results) available on the web. Edgeworth series notes
corrected Nov. 2
*

*
*

- A handout on multivariate
Taylor expansion (and a multivariate g prime-theorem) is available.

- A handout on exponential
families is available.

- A handout on
the saddlepoint approximation of the mle in an exponential family is
now available.

- The final exams from 1988, 1989 and 1995 are available. Some of the problems are concerned with material that we will not cover this quarter, but it should give you a general idea of how my exams tend to look.

I will be trying to stray a little from the usual theorem-proof lecture
style. We will do a group research project,
where the students need to search the literature, devise approaches to a
given problem, assess the quality of their solutions, and present their
work to the class. We will also spend considerable time in class discussing
ways to solve homework problems. Rather than handing in homework solutions
to be graded, the students will usually be presenting and discussing their solutions
in class. In order to get some feedback, two homework sets will be graded.
Part of your grade will be based on your presentation and participation
in the discussions.

Syllabus

Research Projects **
Schedule of
presentations** is now available.

Help is available on the following topics:

- Basic information about web browsers.
- Information about the HyperText Markup Language ( HTML)
- Uniform Resource Locators (URL)
- How to read the web from home using Lynx, a character-based web browser

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