Description

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

• Deciding between Two Simple Hypotheses: The Neyman-Pearson Lemma
• Decision Theory
• The Sequential Probability Ratio Test
• Sequential Decision Theory
• Sufficient Statistics
• Estimation and Convexity
• Minimal Sufficiency and the Lehmann-Scheffé Property
• Lower bounds on Mean-squared Errors: Information Inequalities
• Exponential Families
• Stein's Phenomenon and James-Stein Estimators
• M-estimators and Their Consistency
• Robustness, Breakdown Points, and 1-dimensional Location M-estimates
• Asymptotic Normality of M-estimates
• Efficiency of Estimators

Prerequisite

One semester beginning graduate real analysis and measure theory, as in MIT course 18.125, specifically Chapters 1-5 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.