Texts: required Jun Shao, Mathematical Statistics,
2nd ed., Springer, 2003.
(recommended) Peter Bickel
and Kjell Doksum, Mathematical Statistics, vol.I, 2nd ed., 2007.
V. Rohatgi and A.K. Saleh, An Introduction to Probability and Statistics,
2nd ed., Wiley.
Course Grading: there will be assigned and graded homework
due approximately every 1.5 weeks
(probably 7 in all). Homework
will count 40 toward the course grade, Test(s) [1 in-class 20% plus
1
take-home 15%], and final exam will count 25%.
Course Policies:
(I) Homeworks will
generally be due on a Friday, and should be submitted as hard-copy.
If you
will be off-campus then you may submit these electronically, but in that
case you are
expected to hand in a hard-copy at the following class meeting.
(II) Late Homeworks will be
accepted up to one class meeting later than the due date,
but you will lose 20% credit for late submission.
(II) Makeup tests will
not be given except for written medically excused illness.
(III) Ideas may be shared
among students in working on homeworks, but it is essential
that you
write up the solutions explaining the steps and methods fully in your own
words.
For Take-home Test(s), you may not share ideas with each other and
must not accept help from
anyone other than the course instructor.
I. Background on Limit Theory & Asymptotic Inference Criteria
3 Lectures
A. Strong Law of Large Numbers, Multivariate CLT, Delta Method (Shao Sec. 1.5)
B. Asymptotic Distributions and Asymptotic Criteria for Inference (Shao Sec. 2.5)
II. Asymptotic Estimation Theory, part 1
7 Lectures
A. Large sample behavior of Moments Estimators & MLE's in Exponential Families
(Shao Sec. 3.5.2 and 4.4, Bickel & Doksum Ch. 5 through Sec 5.3)
B. Large sample behavior of 1-dim MLE's and related (Min Contrast and M) estimators
(Shao Sec. 4.5, Bickel & Doksum Ch. 5 Sec 5.4)
C. U Statistics
(Shao Sec. 3.2)
III. Asymptotic Estimation Theory, Multivariate
5 Lectures
A. Multidimensional asymptotic theory for MLE and related estimators
(Shao Sec. 4.5, Bickel & Doksum Ch. 6 Sections 1 and 2)
B. Large Sample Tests & Confidence Regions, based on LR, Wald & Score Statistics
(Shao Sec. 6.4.2, Bickel & Doksum Ch. 6 Sec.3)
IV. Asymptotic Nonparametric (Goodness of Fit) Tests
3 Lectures
Shao Sec. 6.5
V. Bootstrap Variances and Confidence Intervals
5 Lectures
Shao Sec. 5.5, 7.4
VI. Miscellaneous Topics (EM, Shrinkage Estimation, Large-Sample Bayes)
4 Lectures
Shao Sec. 4.3 + Notes