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; chisquared and
KolmogorovSmirnov tests for goodnessoffit; the twosample; confidence
and tolerance intervals. Prerequisite: math231 or Math 309. (Semiparametric
modeling and resampling methods (e.g. bootstrap) are also included in the
courses.)
Here is a typical course description of Nonparametric Statistics at
Lehigh University.
Textbooks used for Math/Stat 462 ( Nonparametric Statistics )
at Lehigh University:

"Theory of Rank Tests", by Hajek and Sidak

"Nonparametric Statistics: methods based on ranks", by E. Lehmann

"DistributionFree Statistical Methods", 2nd edition, by J. S. Maritz.

"An Introduction to the Bootstrap", by B. Efron and Tibshirani.
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References
Currently we have covered the following topics:
1. Introduction to OneSample Statistical Problems.
2. Parametric procedures for onesample problems: ttest, tCI, paired
ttest, MLE, etc.
3. What is Nonparametric Statistics?
4. Some nonparametric procedures for onesample problems.
5. Signedtest for paired sample and binomial distribution.
6. Wilcoxon SignedRank test for paired sample.
7. The exact null distribution of Wilcoxon signedrank 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 signedrank statistic and Sign
statistic.
13. Walsh's averages; HodgesLehmann 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
based.
18. Analytical bootstrap vs simulation based bootstrap.
19. Comparison of HodgesLehmann estimator and sample median (when estimating
the center of symmetry) under contaminated normal models.
20. Efficacies for Wilcoxon's SignedRank 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
Statistics Links
A Casebook in Statistics
and Data Analysis
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WEIMIN HUANG
Professor, Department of Mathematics
Lehigh University