Welcome to CSI 972 / IT 972

Mathematical Statistics I

Fall, 2001

Wednesday, 7:20-10:00pm, Krug Hall 7

If you send email to the instructor, please put "CSI 972" in the subject line.

This course is on the theory of estimation. The principles of estimation are explored including the method of moments, least squares, maximum likelihood, and maximum entropy methods. The methods of minimum variance unbiased estimation are covered in detail. Topics include sufficiency and completeness of statistics, Fisher information, Cramer-Rao bounds, Bhattacharyya bounds, asymptotic consistency and distributions, statistical decision theory, minimax and Bayesian decision rules, and applications to engineering and scientific problems.

The text is Theory of Point Estimation by Lehmann and Casella.

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)

a midterm consisting of an in-class component and a take-home component (30)

a final exam consisting of an in-class component and a take-home component (45)

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

Week 1, Aug 29
Preparations (Lehmann and Casella Sections 1.1 through 1.5).
Assignment 1: page 62, problems 1.2, 1.3, 1.4, 1.7, 1.11, 4.1, 4.2, 4.3, 4.6, 4.8, 4.13, 5.3, 5.6, 5.13, 5.18 (due Sep 12).
Week 2, Sep 6
Sufficiency; loss functions (Lehmann and Casella Sections 1.6 and 1.7).
Assignment 2: page 69, problems 6.2, 6.3, 6.7, 6.16, 6.17, 6.18, 6.30, 6.35, 7.8, 7.14 (due Sep 19).
Week 3, Sep 12
Convergence in probability and in law (Lehmann and Casella Section 1.8).
Assignment 3 page 75, problems 8.1, 8.5, 8.7, 8.11, 8.13, 8.17, 8.18, 8.21, 8.25 (due Sep 26).
Week 4, Sep 19
UMVU estimators (Lehmann and Casella Sections 2.1, 2.2).
Assignment 4: page 129, problems 1.3, 1.4, 1.5, 1.10, 1.13, 1.18, 1.20, 2.1, 2.18, 2.26, 2.27, and 3.2 and 3.23 (due Oct 10).
Week 5, Sep 26
UMVU estimators (Lehmann and Casella Sections 2.1 through 2.5).
Week 6, Oct 3
UMVU estimators; the information inequality (Lehmann and Casella Sections 2.5 and 2.6).
Assignment 5: page 137, problems 4.1, 4.5, 4.6, 5.2, 5.3, 5.7, 5.16, 5.19, 6.2, 6.10 (due Oct 17).
Week 7, Oct 10
Review homework and material in first two chapters. Comments on Assignment 5:
Week 8, Oct 17
More review.
Equivariance (Lehmann and Casella Chapter 3).
Handout take-home portion of midterm.
Week 9, Oct 24
In-class portion of midterm
Take-home portion of midterm due.
Week 10, Oct 31
Review midterm.
Equivariance (Lehmann and Casella Chapter 3).
Assignment 6: page 207, problems 1.3, 1.5, 1.13, 2.1, 2.10, 3.2, 3.28, 4.1, 41.6 (due Nov 14).
Comments (incomplete)
Week 11, Nov 7
Average risk optimality; Bayesian inference (Lehmann and Casella Chapter 4).
Assignment 7: page 282, problems 1.2, 1.3, 1.4, 2.1, 2.3, 2.4, 2.15, 2.16, 3.2, 3.9 (due Nov 28).
Assignment 7 and 7a.
Comments (incomplete)
Week 12, Nov 14
Average risk optimality; Bayesian inference (Lehmann and Casella Chapter 4).
Assignment 7a: page 286, problems 3.12, 5.4, 5.9 (due Nov 28).
Nov 21, No class (Columbus day holiday).
Week 13, Nov 28
Minimaxity and admissability (selections from Lehmann and Casella Chapter 5).
Assignment 8: page 389, problems 1.1, 1.2, 1.7, 1.21, 2.2, 2.23, 3.3, 4.14
Comments (incomplete)
Week 14, Dec 5
More on minimaxity and admissability
Review
Handout take-home portion of midterm.
If you have any questions, or if you think you might have found a typo, please email me.

Exam December 12, 7:30