Description
This graduate level course on Mathematical Statistics includes the following topics:

Deciding between Two Simple Hypotheses: The NeymanPearson Lemma

Decision Theory

The Sequential Probability Ratio Test
Sequential Decision Theory
Sufficient Statistics
Estimation and Convexity
Minimal Sufficiency and the LehmannScheffé Property
Lower bounds on Meansquared Errors: Information Inequalities
Exponential Families
Stein's Phenomenon and JamesStein Estimators
Mestimators and Their Consistency
Robustness, Breakdown Points, and 1dimensional Location Mestimates
Asymptotic Normality of Mestimates
Efficiency of Estimators
Prerequisite
One semester beginning graduate real analysis and measure theory, as in MIT course 18.125, specifically Chapters 15 of the book Real Analysis and Probability, by R. Dudley, 2nd ed., Cambridge University Press, 2002. One or more previous courses in probability or statistics will be helpful background but are not required.
Text
Printed lecture notes (sections from a book in progress) will be distributed as we go along.
Problem Sets and Exams
There will be problem sets, a midterm exam, and a final exam. Students with A’s on the midterm and A averages on the first 7 problem sets will have the option of writing an expository term paper instead of doing the last three problem sets and taking the final exam.
Grading
The grade will be based 50% on problem sets and 50% on either the final exam or a term paper.