Stat 611 -- Winter 2009

STATISTICS 611:

INSTRUCTOR: MOULINATH BANERJEE

INSTRUCTOR OFFICE HOURS: Tue & Thurs, 2:30 to 4:00 p.m., 451, West Hall. Class meets Tue & Thurs from 10:00 a.m. to 11:30 a.m, B760, East Hall

GSI AND GRADER INFO: Toshiya Hoshikawa(toshiyah@umich.edu). Office hours: 2:30 to 4:00 pm, Monday.

EXAM SCHEDULE: Midterm: Tuesday, March 3rd in class (we may start earlier than 10:00). Final: Date, time and place to be announced.

Weightage scheme: 5 homeworks carrying 5 points each + midterm carrying 30 points + final carrying 45 points.

TEXT: Keener's lecture notes (relevant chapters 9, 10 and partly 17, 18) + Ferguson's "A Course in Large Sample Theory" + Notes posted below. Other sources to be used now and then are: some of Wellner's notes below + Lehmann and Cassella (Point Estimation) + Lehmann and Romano (Testing Statistical Hypothesis) + Lehmann's "A Course In Large Sample Theory".

CONTENT: Modes of convergence of random variables, convergence in law and CLTs, delta method, asymptotics of maximum likelihood estimation, likelihood ratio statistics, contiguity theory, EM algorithm + other topics.

Stat 612 Notes: 0

Stat 612 Notes: 1

Stat 612 Notes: 2

Stat 612 Notes: 3

Invariance of information bounds and influence functions under reparametrization

Examples -- 1

Homework 1. Due Feb 12

Homework 1 solutions.

Homework 2.

Homework 3: Problems (a) through (g) from Stat 612 Notes: 0.

Homework 3 solutions.

Homework 4 solutions.

Midterm solutions.

Homework 4: Problems 1, 3, 4, 5 from Stat 612 Notes: 2. Due by 4:00 p.m. April 10th, 439 West Hall.

SUPPLEMENTARY NOTES: (courtesy Jon A. Wellner; also available on last semester's 610 webpage)

The Probability Background

Important distributions in Statistics.

Basic Large Sample Theory.

Lower Bounds For Estimation.

Efficient Likelihood Estimation and Related Tests.

Bayes Methods and Decision Theory.

Hypothesis Testing.

Statistical Functionals and the Delta Method.

The Bootstrap and the Jackknife.

Sufficiency and Unbiased estimation.

ANNOUNCEMENT: