Math 408 - Nonparametric Statistics - Spring 2009

Statistical methods that make minimal assumptions about the probability distribution of data.

Topics covered:

Sign test, Wilcoxon signed rank and rank sum tests, nonparametric confidence intervals, jackknife and bootstrap methods, Kruskal-Wallis and Jonckheere-Terpstra tests (like a one-way ANOVA), Friedman and Lehmann aligned-rank tests (like a two-way ANOVA), Spearman and Kendall correlation coefficients, Kolmogorov-Smirnov tests, and topics chosen from nonparametric regressions and nonparametric density estimation.
MATLAB programs will be used to evaluate the accuracy of large-sample approximations for nonparametric tests and to carry out statistical procedures that cannot easily be done by hand. Sample MATLAB programs will be posted on the Web site to illustrate the programming techniques used (and to show how to use MATLAB). Prior experience with MATLAB (or C or a related language) would be helpful but is not assumed.

Prerequisites: Mathematics 420 or 493, or permission of the instructor.
Time and Location:   TTh 2:30-4:00pm -- Cupples I  Rm 218
Textbook: Nonparametric Statistical Methods, 2nd edition,
M. Hollander and Douglas A. Wolfe (1999) (Wiley)   ISBN 0-471-19045-4
Instructor: Prof. Stanley Sawyer -- Cupples I, Room 107
Phone: (314) 935-6703   --   Send an email
Office Hours: MW 6:00-7:00pm   Office:  Cupples I  Rm 107
(Warn me in advance if you are coming  --  other times are OK by appointment)
TAKE-HOME FINAL: Due by Wednesday May 6 at 4:30 pm   Cupples I Rm 100 or Rm 107
Links: Homework Assignments
Example MATLAB programs
HINTS for using MATLAB
Bootstrap handout (PDF)
Jackknife handout (PDF)
Rank-regression handout (PDF)
Stanley Sawyer's home page
Mathematics Department Home Page
Washington University Home Page

SEE BELOW for some optional but useful references.

Homework Sets, Exams, and Grades:
        There will be around five homework sets, an in-class midterm, and a final. Grades will be based on on the homework sets (around 40%), the midterm (around 20%), and the final (around 40%). Cr means D or better if you elect ``Credit/No Credit.''

Collaboration:
        Collaboration on homework is allowed and can be helpful (and fun). However, you must (i) write the names of the people that you collaborated with at the top of your homework and (ii) write up your homework in your own words.

Warning:
        Make a copy of each homework before you hand it in!!
        It may not be returned before you need to refer to it for the next homework (or for the next test).

NOTE:   If you use a computer to do a homework problem, then hand in (in the following order):
        (i) your answers to the homework problems, with references to page numbers in part (iii) if your answer depends on your computer output and the output has more than one or two pages,
        (ii) the source code for the computer program or programs that you used in part (i), and
        (iii) the computer output on which you based your answers in part (i), with hand-written (or other) page numbers that you can use in part (i).

REFERENCES:

A Useful Introduction/Reference Manual for MATLAB:
        MATLAB: An Introduction with Applications
        Amos Gilat (2008) (Wiley)

A Reference for Nonparametric Statistics:
        Nonparametrics: Statistical Methods Based on Ranks
        E. L. Lehmann (1975) (Holden-Day/McGraw-Hill)
        This is a standard advanced book on nonparametric statistics.

Scientific Programming:
        Numerical Recipes: the Art of Scientific Computing, 3rd edition
        W. Press, S. Teukolsky, W. Vetterling, and B. Flannery (2007) (Cambridge University Press)

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Click here for Stanley Sawyer's home page:

Last modified April 13, 2009