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 courses.)

Here is a typical course description of Nonparametric Statistics at Lehigh University.

Textbooks used for Math/Stat 462 ( Nonparametric Statistics ) at Lehigh University:

Click for Lehigh's home page or for Lehigh Mathematics Department home page.


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 statistic.
  • 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 based.
  • 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

  • Statistics Links
  • A Casebook in Statistics and Data Analysis



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    Professor, Department of Mathematics
    Lehigh University