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

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.