Statistics 561

Fall Semester 1997, Spring 1998

Instructor: Bing Li; Telephone: 865 1952; Office: 410 Thomas Building.

Time: MWF 1:25 pm - 2:15 pm

Place:110 Thomas Building

Office hours: MWF 4:00pm - 5:00pm.

Texts and references:

• Mathematical Statistics: A Decision Theoretic Approach, Thomas Ferguson.
• Theory of Point Estimation, Erich Lehmann.
• Testing Statistical Hypothesis, 2nd edition, Erich Lehmann (reference).
• Approximation Theorems of Mathematical Statistics, Robert Serfling (reference).
• Quasi-likelihood and its application, Christopher Heyde (reference).
• Tensor methods in Statistics, Peter McCullagh (reference).

Course coverage:

Statistics 561 -- Finite sample theory of statistical inference

• Basic ideas of decision theory (Chapter 1,2 of Ferguson).
• Point estimation (Chapter 3 of Ferguson).
• Hypothesis testing (Chapter 5 of Ferguson).
• Invariant estimation and test (Chapter 4 and part of Chapter 5 of Ferguson).

Statistics 562 -- Large sample theory of statistical inference

• Elementary limit theorems (Serfling).
• Maximum likelihood estimation. (Wald 1949, Wolfowitz 1949, Lehmann Chapter 5-6).
• General theory of estimating equations.
• Likelihood ratio test, Wald test, and Rao's score test.
• Local analysis of test statistics. (Hall & Mathiason 1990, Bahadur 1964).
• Asymptotic expansions. (McCullagh 1987)

Examinations: There will be a midterm and a final exam for each semester. They will be closed book and in class. You may bring a page of prepared notes for each exam.

Assignments: Homework will be assigned and graded every two weeks.

Evaluation: Midterm 30 %. Final 45%. Homework 25%.