Statistics 528

Introduction to Mathematical Statistics

Spring 2007

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Course outline

This course introduces the basic concepts and techniques in mathematical statistics. We will start with a review of basic probability theory, then delve into the formulations of problems, the estimation techniques, and the hypothesis testing techniques. Among topics to be covered are normal and derivative (chi-square, F, and t) distributions, exponential families, sufficiency, unbiased estimation and information inequality, maximum likelihood estimation and its efficiency, confidence intervals and hypothesis testing, log likelihood ratio tests, asymptotic approximations, etc. There will also be brief discussions of Bayesian methods and decision theory.

Prerequisite

Basic probability theory (STAT 519 or equivalent). Working knowledge of advanced calculus, linear algebra, and matrix theory.

Textbook

• Mathematical Statistics (2nd ed.), by Bickel and Doksum

References

• Statistical Inference, by Casella and Berger.
• Theoretical Statistics, by Cox and Hinkley.
• Introduction to Mathematical Statistics, by Hogg and Craig.
• Linear Statistical Inference and Its Applications, by Rao.
• Statistical Inference, by Silvey.

Course Work

Weekly/biweekly homework problems will be assigned through the semester, accounting for 30\% of the course grade.

There will be two midterm exams, each accounting for 20\% of the course grade, and a final exam, accounting for 30\% of the course grade.

You are encouraged to discuss with each other on the homework assignments, but you are expected to do your independent work.

Lecture Notes

Homework Assignments