Math 462 & Stat 462 at Lehigh University
Math 462/Stat 462 (Nonparametric Statistics): Order and rank statistics;
tests based on runs, signs, ranks, and order statistics; chi-squared and
Kolmogorov-Smirnov tests for goodness-of-fit; the two-sample; confidence
and tolerance intervals. Prerequisite: math231 or Math 309. (Semiparametric
modeling and resampling methods (e.g. bootstrap) are also included in the
Here is a typical course description of Nonparametric Statistics at
Textbooks used for Math/Stat 462 ( Nonparametric Statistics )
at Lehigh University:
Click for Lehigh's home page or for
"Theory of Rank Tests", by Hajek and Sidak
"Nonparametric Statistics: methods based on ranks", by E. Lehmann
"Distribution-Free Statistical Methods", 2nd edition, by J. S. Maritz.
"An Introduction to the Bootstrap", by B. Efron and Tibshirani.
Currently we have covered the following topics:
1. Introduction to One-Sample Statistical Problems.
2. Parametric procedures for one-sample problems: t-test, t-CI, paired
t-test, MLE, etc.
3. What is Nonparametric Statistics?
4. Some nonparametric procedures for one-sample problems.
5. Signed-test for paired sample and binomial distribution.
6. Wilcoxon Signed-Rank test for paired sample.
7. The exact null distribution of Wilcoxon signed-rank statistic.
8. Normal approximation to null distribution of Wilcoxon statistic.
9. Sampling from finite populations.
10. The concept of scoring (Wilcoxon scores, normal scores, ....).
11. A class of linear rank statistics.
12. Confidence intervals based on Wilcoxon signed-rank statistic and Sign
13. Walsh's averages; Hodges-Lehmann estimator and its standard deviation.
14. Statistical functionals and estimating equations.
15. A general formula for determining the 1st order approximation of the
s.d. of an estimator.
16. Difficulties in finding analytical forms of s.d.'s for complexed estimators.
17. Some resampling methods: permutation based, jackknife based, bootstrap
18. Analytical bootstrap vs simulation based bootstrap.
19. Comparison of Hodges-Lehmann estimator and sample median (when estimating
the center of symmetry) under contaminated normal models.
20. Efficacies for Wilcoxon's Signed-Rank based, Sign based, Mean based
and MLE based statistical procedures.
21. Local asymptotic powers and its relationship to asymptotic efficacies.
22. Estimation of CDF (Parametric vs Nonparametric).
23. Empirical CDF, Empirical process and Brownian Bridge Process.
24. Empirical CDF Based Statistical Functionals, Weak Convergence, Exact
vs Asymptotic Distributions.
Statistics Related Links
A Casebook in Statistics
and Data Analysis
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Professor, Department of Mathematics