Lehigh's Math 312

Fall 2000 Math 312 / STAT 412 at Lehigh University

This is the home page for Fall 2000 Math 312 / STAT 412 ( Computational Statistics ) at Lehigh University.

Textbook: Lecture Notes in Statistical Methods

More information will follow later (or call me at (610) 758-3735).

Instructor: Professor Wei-Min Huang, Department of Mathematics. To contact me, send e-mail to wh02@Lehigh.EDU, or click here Mail-Me, if your web server supports forms. Click for Lehigh's home page or for Lehigh Mathematics Department home page.

Course Description (see handout)

Homework Assignments & Exercises (see handout)

Currently we have covered the following topics:

  • 0. Introduction to statistical methods.
  • 1. Review of basic probability distributions and basic statistical methods.
  • 2. Some standard probabilistic results used in statistics.
  • 3. Introduction to one-sample statististical problems.
  • 4. Normal-model and t-statistic
  • 5. When do we use t-statistic? What are the other options?
  • 6. Tests for normality
  • 6a. Kolmogorov-Smirnov statistic
  • 6b. Anderson-Darling statistic
  • 6c. Cremer-von Mises statistic
  • 6d. Shapiro-Wilk statistic (and correlation based statistic)
  • 6e. Simulation study on the distribution of K-S statistic
  • 7. Introduction to two-sample problems
  • 8. Ten useful statistical models for two-sample problems
  • 9. Two-sample t-statistic
  • 10 Two-sample F-statistic
  • 11. Two-sample Mann-Whitney-Wilcoxon ranksum statistic
  • 11a. Shift-model
  • 11b. Exact and asymptotic distribution
  • 11c. View it as a permutation test
  • 11d. View it as a resampling (without replacement) procedure
  • 12. Two-sample Tukey-Siegel ranksum statistic
  • 12a. Scale-model
  • 12b. Just a different way of ranking the observations
  • 13. Exact and approximate sampling distributions of ranksum statistic
  • 14. Kolmogorov-Smornov statistic & empirical process
  • 15. Anderson-Darling statistic & empirical process
  • 16. Cramer-von Mises statistic & empirical process
  • 17. Paired-sample problem
  • 17a. Normal theory procedures
  • 17b. Procedure based on sign
  • 17b. Procedures based on sign and rank (Wilcoxon signed-rank statistic)
  • 17c. Walsh's averages and confidence interval for the shift-parameter
  • 17d. Construct you own test for symmetry
  • 18. Methods of Estimation
  • 18a. Method of Least-Squres
  • 18b. Method of moments
  • 18c. Minimun ch-squared estimate
  • 18d. Maximun Likelihood Estimate
  • 18e. Asymptotic results for maximun likelihood estimate
  • 18f. Bootstrap the MLE
  • 19. Simple linear regression model (with normality)
  • 20. Nonparametric simple linear regression model (rank based)
  • 21. Logistic Regression.
  • 22.
  • 23.
  • 24.

    Statistics Related Links

  • Statistics Links

  • A Casebook in Statistics and Data Analysis

    To go back to my homepage click here

    To return to Lehigh's home page, click here.

    WEI-MIN HUANG
    Professor, Department of Mathematics
    Lehigh University