Welcome to CSI 973 / IT 973
Mathematical Statistics II
Spring, 2004
Tuesday, 7:20-10:00pm, Innovation Hall, room 137
Instructor:
James Gentle
If you send email to the instructor,
please put "CSI 973" in the subject line.
This course is part of a two-course sequence.
The general description of the two courses is available at
www.scs.gmu.edu/~jgentle/csi9723/
This course resumes where CSI 972 ends (which in Fall, 2003, was at the
end of Section 4.3 in Shao).
The course begins with a brief review of the
general theory of statistical estimation, and estimation in parametric
models. It then continues with maximum likelihood estimation and
asymptotic properties of estimators in parametric
models. Next, estimation in nonparametric models is covered.
Hypothesis tests and confidence intervals are then covered.
The text is Jun Shao (2003), Mathematical Statistics,
second edition, Springer.
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,
and there may be some slight adjustments.
Occasionally, I will post some ``follow-up lecture notes''.
- Week 1, January 20
Review general principles of estimation.
Maximum likelihood estimation (Shao, Section 4.4).
Assignment 1 (due Feb 10): Exercises 4.6, beginning on page 299:
94, 95, 96(a),96(g), 96(h), 97, 109, 113, 118, 120, 140, 152.
- January 27
Class canceled because of weather.
- Week 2, February 3
Discuss handout on MLE.
- The likelihood principle.
- Computational issues.
- EM.
- Asymptotic properties of MLEs.
- Problems with MLEs. Counterexamples.
- Week 3, February 10
Estimation in nonparametric models.
- The ECDF and some pointwise properties.
- Norms and metrics, with applications to CDFs.
- The Glivenko-Cantelli theorem.
- Empirical likelihood and examples.
- Nonparametric probability density estimation.
- Partial likelihood and profile likelihood.
- Statistical functionals.
Assignment 2 (due Mar 2): Exercises 5.6, beginning on page 383:
3, 5, 9, 17, 20, 21, 24, 27, 39, 59, 61, 63, 74, 86, 90, 96, 111
- Week 4, February 17
Estimation in nonparametric models continued
- Statistical functionals, and estimation based on them.
- Differentiation of functionals.
- Some useful statistical functionals: L, M, and R estimators.
- Week 5, February 24
Estimation in nonparametric models continued; GEE.
Variance estimation.
- Week 6, March 2
Review estimation principles.
Work some problems.
Ch 4: 118 Li; 152 (b) Weijie;
Ch 5: 63 Chunling; 86 Eoh; 96 Nan.
Hand out take-home portion of midterm.
- March 9
Spring recess; class does not meet.
- Week 7, March 16
In-class portion of midterm.
You can use one sheet of prewritten notes.
Take-home portion of midterm due.
- Week 8, March 23
Hypothesis testing: UMP tests; Neyman-Pearson theory; UMPU tests; UMPI tests.
Assignment 3 (due April 6): Exercises 6.6, beginning on page 454:
1, 4, 5(a), 5(b), 12, 17, 27, 29, 37, 38, 51, 52(a), 58, 63, 69(a), 74, 93, 98, 107
- Week 9, March 30
Hypothesis testing: parametric tests; LR, Wald, score tests;
nonparametric tests; asymptotic properties.
- Week 10, April 6
Hypothesis testing continued
Confidence sets: basic methods of constructing and basic properties.
Assignment 4 (due April 27): Exercises 7.6, beginning on page 527:
1, 2, 9, 18, 28, 29, 31, 40, 44, 48, 60, 63, 67, 79, 82, 93, 95, 101
- Week 11, April 13
Confidence sets continued
- Week 12, April 20
Confidence sets continued
- Week 13, April 27
Confidence sets continued
- Week 14, May 4
Confidence sets continued
Review
Handout
take-home portion of exam
Exam May 11, 7:30