I will try my best to make this page as accurate as possible but any
changes
in assignments, due dates, or anything else reported in class will take
precedence,
whether they are reflected in these pages or not. Your responsibilities
are as they are reported in class.
Fall, 2007 STA 662 - 001 Bootstrap and
Other
Re-sampling Methods
Instructor: Dr. Mai Zhou
Office: P. O. T. 849, Mailbox: P. O. T. 843, Phone: 257-6912,
E-mail:
mai@ms.uky.edu, Web page (this page):
http://www.ms.uky.edu/~mai/sta662.html
Office Hours: TBA or by appointment.
Class: MWF 1:00 PM -- 1:50 PM at CB 307.
Final Exam: 1:00PM Dec.14, 2007.
Textbook: An
Introduction to the Bootstrap by Efron and Tibshirani.
Chapman Hall/CRC 1993.
Reference books: Bootstrap Methods and their Applications
by Davison and Hinkley. Cambridge Univ. Press, 1997.
(more theoretical) The
bootstrap and Edgeworth Expansion by P. Hall. Springer
1992.
Computing: The ability to
perform repetitive computations quickly is essential to this course.
Some examples
of statistical/mathematical
packages useful are: R/Splus, SAS, MatLab.
Course Description: The
Bootstrap and other re-sampling methods, hailed by some as the ``New
Statistics" that ``revolutionized 1990's statistics" is a method made
practical by the vastly improved computing powers. I shall try to
explain in this course:
- What is the bootstrap method? What can it do? What is the
difference of bootstrap and Monte Carlo simulation? The bootstrap
idea and examples of bootstrap in action.
- Parametric and nonparametric bootstrap. Empirical distributions.
Sampling from empirical distribution. Plug-in principle.
- Bootstrap estimation of bias and bias correction.
- Bootstrap confidence intervals: BCa and
bootstrap t confidence interval.
- Why bootstrap is ``better'' (better than what)? Error analysis in
the bootstrap. Speed of convergence. Some basic theoretical foundation
of the bootstrap method will be studied along with necessary tools. We
proof that the bootstrap can produce a more accurate confidence
interval than would otherwise based on the usual normal approximation
(central limit theorem). (The detailed proof of this may be beyond Sta
601, but skipping the proof do not hurt the understanding of the rest
of the course). We also provide a heuristic explaination.
- Bootstrap and the estimation equation
- Some further applications of bootstrap: bootstrap tests,
adjusted p-value, bootstrap regression models.
- Examples that bootstrap fail.
- Jackknife and other re-sampling methods. Its relation to
the
bootstrap.
- Bootstrap and censored data.
- Better bootstrap computations.
- Introduction to Empirical Likelihood method and Bootstrap
calibration of Empirical likelihood ratio. (If
time permits)
The following notes may be useful:
What can simulations do? Note1
Some examples of second order accuracy of parametric bootstrap
Note2
Empirical distributions or sampling distributions.
A note by
H. White
A note about empirical likelihood and
bootstrap
A chapter about bootstrap
Some tips about
efficient R programming
Homework
exam
Example of bootstrap regression, 1
2
and
3
Example of bootstrap logistic regression
Example of using control function
as in re-centering
Example of Importance sampling,
as in nonparametric bootstrap
Example of skewness
Evaluations:
Homework + a project 50%
Midterm Exam 20%
Final Exam 30%
Make-up Policy for Missed Exams: Make-up
quizzes and exams will
be given only for university excused absences. Requests must be made at
least one week prior to the exam, when possible, and must be approved.
If you are unable to attend and exam due to unforeseen circumstances
you
must contact me or the department office (257-6115) as soon as possible
(within 2 days).
Absences due to illness must be documented by a clinic, doctor or
hospital
visit and a note of explanation. Late homework and computer assignments
will be accepted only for university excused absences.