Welcome to CSI 973 / STAT 973 / IT 973

Mathematical Statistics II

Spring, 2008

Monday, 4:30-7:10pm, Enterprise Hall, room 178

Instructor: James Gentle

Appointments for individual consultations can be made by email to the instructor.

Some of the lectures will be based on the instructor's notes posted on this website. Some lectures will be accompanied only by notes written on the board.

Recitations (optional): Monday, 7:30pm, Research Building I, room 92

During the optional recitation periods students and/or the instructor will discuss exercises, especially those listed as "for practice and discussion". The instructor may also discuss some of the class notes.

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

A useful supplement is Jun Shao (2005), Mathematical Statistics: Exercises and Solutions, Springer. My assigned "exercises for practice and discussion" are all solved (or at least partially solved) in this book.
See also the references listed in the general description.

This course resumes where CSI 972 ended (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.

I have put together a set of notes to supplement the material in the text and the lectures. These notes have a subject index that should be useful. (I am continually working on these notes, so they may change from week to week.)

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)

    Each homework will be graded based on 100 points, and 5 points will be deducted for each day that the homework is late.

    Each student enrolled in this course must assume the responsibilities of an active participant in GMU's scholarly community in which everyone's academic work and behavior are held to the highest standards of honesty. The GMU policy on academic conduct will be followed in this course.

    Except during a period between when a take-home exam has been given out and when the exam is due, students are free to discuss the homework with each other or anyone else, and are free to use any reference sources. Explicit copying should not be done.

    Students are not to communicate concerning exams with each other or with any person other than the instructor. On take-home exams, any passive reference is permissible (that is, the student cannot ask someone for information, but the student may use any existing information from whatever source). During a period between when a take-home exam has been given out and when the exam is due, students are not to discuss with each other any aspect of the course -- homework, examples, or anything else relating to the course in any way. Any violation of this rule is a violation of the GMU Honor Code.

    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 28

    Review CSI972 inclass final.
    Review principles and procedures of statistical estimation and other relevant material from CSI 972.
    Asymptotic efficiency.
    Maximum likelihood estimation.
    Reading assignment: Read Shao, Chapter 4.
    Exercises assignment for practice and discussion: In Exercises 4.6: 96(a)(g)(h), 107, 151.
    Assignment 1, due Feb 18: In Exercises 4.6: 94, 95, 97, 109, 120, 152.

    Week 2, February 4

    Maximum likelihood estimation.

    EM examples. (Read general notes on optimization.)

    Week 3, February 11

    Maximum likelihood estimation.

    The Bayesian approach; Bayesian estimation (review from MathStat_I, pp 77-95)

    Reading assignment: Read Shao, Sections 4.1, 6.4.4, and 7.1.3.
    Assignment 2, due Mar 3: In Exercises 4.6: 31, 32 (note typo for (b) and (c)); in Exercises 6.6: 106, 107; in Exercises 7.6: 28, 29.
    May turn in as late as March 7. Comments.

    Week 4, February 18

    Bayesian approaches to hypothesis testing.

    Week 5, February 25

    Bayesian credible sets.
    Followup comments on MLEs in parametric ranges.
    Hand out midterm takehome.
    Between now and the end of class on March 3, students are not to discuss homework or other aspects of the course (including the takehome of course!) with anyone other than the instructor.

    Week 6, March 3

    Midterm exam.
    Closed book and closed notes except for one sheet (front and back) of prewritten notes.
    Reading assignment: Read Shao, Chapter 6.
    Exercises assignment for practice and discussion: In Exercises 6.6: 2, 3, 4, 6, 10, 17,20, 29,37, 51, 52, 58, 93, 98, 123
    Assignment 3, due April 14: Exercises 6.6, beginning on page 454:
    1, 5(a), 5(b), 5(c), 12, 21, 23, 27(a), 27(b), 27(c), 38, 52(a), 52(b), 63, 69(a), 74, 92(a), 92(b), 99(a), 99(b), 107

    (No Class March 10)

    Week 7, March 17

    Review midterm.
    Hypothesis testing.
    Because of St Patrick's Day, there will be no recitation session this evening.

    Week 8, March 24

    Review midterm takehome.
    UMP tests; Neyman-Pearson theory
    UMP tests in exponential families.
    LR tests.
    Asymptotic properties.
    Wald and score tests.
    Reading assignment: Read Shao, Chapter 7.
    Exercises assignment for practice and discussion: In Exercises 7.6: 9, 18, 29, 31, 48, 60, 63, 67
    Assignment 4, due April 21: Exercises 7.6, beginning on page 527:
    1, 2, 28, 40, 44, 79, 82, 93, 95, 101

    Week 9, March 31

    Confidence sets.

    Week 10, April 7

    Confidence sets continued; bootstrap methods.
    Reading assignment: Read Shao, Chapter 5.

    Week 11, April 14

    Estimation in nonparametric models.
    Assignment 5, due May 5: Exercises 5.6, beginning on page 383:
    3, 5, 9, 17, 20, 21, 24, 27, 39, 59, 61, 63, 74, 86 90, 96, 111 (note typo: \hat{c}_4 should be \hat{c}_4 - \hat{c}_2^2

    Week 12, April 21

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

    Week 13, April 28

    Estimation of functions.
    Nonparametric density estimation.

    CSI973 take-home final.

    Week 14, May 5

    May 12

    4:30pm - 7:15pm Final Exam.
    Closed book and closed notes except for one sheet of prewritten notes.