Welcome to CSI 973 / IT 973

Mathematical Statistics II

Spring, 2002

Wednesday, 7:20-10:00pm, 260 Science and Technology II

If you send email to the instructor, please put "CSI 973" in the subject line.

This course is on the theory of statistical inference, particularly hypothesis testing. Topics include characterization of the decision process, the Neyman-Pearson lemma and uniformly most powerful tests, confidence sets, unbiasedness of inference, and invariance of inference. Both the Neyman-Pearson formulation and the Wald decision function approach to testing will be discussed. The emphasis is on frequentist approaches, but Bayesian approaches will also be covered.

The texts are Testing Statistical Hypotheses (TSH) by Lehmann and Theory of Point Estimation (TPE) by Lehmann and Casella. (See additional references below.)

Student work in the course (and the relative weighting of this work in the overall grade) will consist of

a number of small assignments, problems, etc. (25)

an in-class midterm (20)

a final exam consisting of an in-class component and a take-home component (55)

Schedule

An approximate schedule is shown below. As the semester progresses, more details will be provided on the topics to be covered.

Week 1 (January 23)
Review of some of the basics of probability and mathematical statistics.
The general decision problem; terminology (TSH Chapters 1 and 2, and handouts).
Assignment: Read TSH Chapters 1 and 2. Work problems 2, 3, 5, 6, 8, 9, 10, 11 and 14 in Chapter 1 (beginning on page 23), and problem 2 in Chapter 2 (page 60). (Problem Set 1) In most cases, the statement of the problem leaves out the (obvious?) phrase "Show that ..."
Problems due Feb 6.
Week 2 (January 30)
Asymptotic optimality. (This is material from TPE that I feel we should cover before proceeding. TSH has only minimal discussion of asymptotics.)
Assignment: In TPE, Chapter 6, Problems 1.1, 1.11, 2.11, 3.15, 4.18, 4.19, 6.1, 6.2, 6.3, 6.5, 6.9, 6.13, 6.14, 7.26, 8.1. (Problem Set 2)
Problems due Feb 13.
Week 3 (February 6)
More on asymptotical optimality (TPE, Chapter 6) Uniformly most powerful tests.
Week 4 (February 13)
Theory of uniformly most powerful tests.
Assignment: Read Chapter 3 in TSH, and work problems 3, 4, 5, 7, 11, 15, 21, 27, 40, 47. (Problem Set 3)
Problems due Feb 27.
Week 5 (February 20)
More on the theory of uniformly most powerful tests.
Week 6 (February 27)
Unbiasedness in testing.
Assignment: Read Chapter 4 in TSH, and work problems 2, 3, 5, 9, 18. (Problem Set 4a)
Problems due Mar 27.
Week 7 (March 6)
More on unbiased tests.
Handout take-home midterm, covering primarily parts of TPE Chapter 6, and TSH Chapters 1, 3, and 4.
The midterm will be due on Mar 20.
The midterm will not take 2 weeks! The 2 weeks is just a consequence of when Spring Break happens to fall, and of my original plan to have the midterm in class.
Spring Break (March 10-17)
Week 8 (March 20)
More on UMPU tests.
Assignment: In Chapter 4 in TSH, work problems 19, 20, 24, 25, 27, 31. (Problem Set 4b)
Problems due Mar 27 (together with those assigned on Feb 27.
Week 9 (March 27)
More on optimal tests.
Bayesian approaches to inference. Risk sets.
Assignment: Read Chapter 5 in TSH, and work problems 1, 2, 4 (Problem Set 5a), plus additional Problem Set 5
Week 10 (April 3)
Review midterm.
Testing hypotheses in multiparamter exponential families.
Week 11 (April 10)
Invariant tests.
Assignment:
Work problems 12, 25, 32, 34 in Chapter 5 in TSH.
Read Chapter 6 in TSH, and work problems 2, 5(i), 6(i), 6(ii) in Chapter 6.
Week 12 (April 17)
Tests in linear models.
Problems 5, 8, 10, 13 in Chapter 7.
Week 13 (April 24)
More on linear hypotheses.
Problems 2, 3, 4 in Chapter 7 -- not to turn in.
Week 14 (May 1)
More on linear hypotheses.
General review and review of assignments.
Handout take-home portion of final (due May 8).

Exam May 8, 7:30