Instructor: James Gentle

If you send email to the instructor, please put "CSI 972" 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/

This course is primarily on the theory of estimation. It begins with a brief discussion of probability theory, and then covers fundamentals of statistical inference. The principles of estimation are then explored systematically. Minimum variance unbiased estimation is covered in detail. Topics include sufficiency and completeness of statistics, Fisher information, bounds on variances, consistency and other asymptotic properties. Other topics and approaches in parametric estimation are covered in detail. Topics include the general formulation of statistical decision theory and optimal decision rules.

The text is Jun Shao (2003), * Mathematical Statistics,
* second edition, Springer.

Be sure to get the corrections at the
author's website

I plan to cover the material through Section 4.3 in 972.

I plan to cover the remainder in 973.

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

For in-class exams, one sheet of notes will be allowed.

An approximate schedule is shown below. As the semester progresses, more details will be provided, and there may be some slight adjustments.

How to learn mathematical statistics (working problems and remembering the big picture); "easy pieces".

Basic math operations, methods of proving statements.

Fundamentals of measure theory: sigma-fields, measures, integration and differentiation.

Fundamentals of probability theory: random variables and probability distributions, and expectation; important inequalities. (Shao, Sections 1.1 and 1.3)

Solutions, comments.

Solutions, comments.

Sequences of sets; intervals on the reals

Continue discussion of fundamentals of probability theory: special stochastic processes, asymptotics. (Shao, through Chapter 1)

Hints, comments.

Handout takehome portion of midterm (remember the username and password).

Sample from a previous year.

Solution/comments. Once you look at this, you destroy the value in the sample.

Sample from a previous year.

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

Comments.

UMVU estimation.

Some basic facts about matrices and vectors

More information about matrices and vectors

Bayesian methods.

Review.

Handout takehome portion of final (due December 14).

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

Sample from a previous year.