# Welcome to CSI 973 / IT 973

## Spring, 2006

Wednesday, 7:20-10:00pm, Innovation Hall, room 207

Instructor: James Gentle

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

This course is the second part of a two-course sequence. The general description of the two courses is available at mason.gmu.edu/~jgentle/csi9723/

The text is Jun Shao (2003), Mathematical Statistics, second edition, Springer.
Be sure to get the corrections at the author's website
This course resumes where CSI 972 ends (which is 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.

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

• homework assignments (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)

For in-class exams, one sheet of notes will be allowed.

An approximate schedule is shown below. As the semester progresses, more details will be provided, and there may be some slight adjustments.

#### Week 1, January 25

Review principles and procedures of statistical estimation.
Maximum likelihood estimation.
Problems assignment 1, due Feb 15: Exercises 4.6, beginning on page 299:
94, 95, 96(a),96(g), 96(h), 97, 109, 118, 120, 152.

#### Week 2, February 1

Maximum likelihood estimation.

#### Week 3, February 8

Maximum likelihood estimation.
• Asymptotic properties of MLEs.
Estimation in nonparametric models.
Assignment 2, due Mar 1 (but can be turned in Mar 8): Exercises 5.6, beginning on page 383:
3, 5, 9, 17, 20, 21, 24, 27, 39, 59, 61, 63, 74, 86

#### Week 4, February 15

Asymptotic properties of MLEs continued.
• Asymptotic relative efficiency.
• Problems 4.6.113 and 4.6.140.

Estimation in nonparametric models continued.

• Empirical likelihood and examples.
• Nonparametric probability density estimation.
• Partial likelihood and profile likelihood.

#### Week 5, February 22

Asymptotic properties continued.
Statistical functionals, and estimation based on them.
Handout takehome portion of midterm, due March 8.

#### Week 6, March 1

Differentiation of functionals.
Some useful statistical functionals: L, M, and R estimators.

#### Week 7, March 8

Midterm exam (through Section 5.3).
Closed book and closed notes except for one sheet (front and back) of prewritten notes.
Sample from a previous year.

#### Week 8, March 22

Review in-class midterm.
Hypothesis testing.
Introduction.
Assignment 3, due April 12: 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 29

Review take-home midterm.
UMP tests; Neyman-Pearson theory
UMP tests in exponential families.

#### Week 10, April 5

UMPU tests; UMPI tests
Parametric tests; LR, Wald, score tests.
Nonparametric tests; asymptotic properties.
Bayesian approaches to hypothesis testing.
Assignment 4, not to be turned in: 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 12

Confidence sets: Introduction.

#### Week 12, April 19

Confidence sets continued: basic methods of constructing and basic properties.
Bootstrap methods.

#### Week 13, April 26

Other topics on confidence sets.
Bayesian credible sets.
Handout takehome portion of final (due May 10).

#### Week 14, May 3

Go over homework (3 and 4).
Review various topics in estimation; GEE; variance estimation.

#### May 10

7:30pm - 10:15pm Final Exam.
Closed book and closed notes except for one sheet of prewritten notes.
Sample from a previous year.