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

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click here

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WEI-MIN HUANG

Professor, Department of Mathematics

Lehigh University