Syllabus and Tutorials (Stat 4033)

Nonparametric Statistics

A better name for this topic is distribution-free Statistics, as we would like to call it. Here are some of the R tutorials in markdown format that I have written for this class.

Most of these examples were collected from various sources / books etc. and I have tried to give credits for each of them. However, if you notice something with a missing citation or you think should not be here, please let me know at jd033@uark.edu.

This website is for class purposes only.

Syllabus

1. Motivation for Nonparametric methods.
2. Review of univariate probability & central limit theorem.
3. Review of parametric inference: Point & interval estimation and Hypothesis testing (P-value).
4. Tests of randomness**
5. Tests of goodness of fit (Chi square goodness-of-fit tests. Kolmogorov-Smirnov goodness-of-fit tests, Lilliefors test for Normality).
6. One-sample and paired-sample procedures (Sign test & the Wilcoxon signed-rank test, normal approximation and continuity correction, calculation of exact P-values).
7. Two-sample problem: Location model, scale model, Permutation test, The Wilcoxon rank-sum test /Mann-Whitney U test, Discuss K-S test for two samples, Calculation of exact P-value and normal approximation. (Equivalence of rank-sum & Mann-Whitney U test). Distribution-free property of Kolmogorov-Smirnov Test Statistics and Asymptotic distribution (Brownian Bridge).
8. Test for scale model: Siegel-Tukey & similar tests* Additional topics: Linear rank tests, van der Waerden test, Asymptotic Relative Efficiency, Randomized Test.
9. Tests of equality of K distributions (Kruskal-Wallis one-way ANOVA)
10. Various nonparametric measures of association (Kendall’s \(\tau\), Spearman’s \(\rho\)).
11. Measures of association in multiple classifications.
12. Bootstrap & other resampling techniques*
13. Analysis of count data*

Apps for fundamental concepts in probability

1. Empirical CDF converges to true CDF
2. Demoivre-Laplace Central Limit Theorem

Beyond basics: Introduction to a few topics in R

1. apply, sapply, lapply and functions in R
2. Updated introduction to advanced topics in R. It’s basically the 2.0 version of (1) above
3. Matrix Example in R, introduction to parallel computing

R Demos

1. Quantile transformation, Random Variable Generation using QT, QQplot and Goodness of fit Examples in R
2. Wilcoxon signed rank test and QQplots/GoF demo Examples
3. One way Analysis of Variance (ANOVA): Examples in R
4. ANOVA in R Demo in ioslides presentation.
5. Tests for trends and associations R Examples, More examples
6. Bootstrap R Examples
7. Chi-square tests R Examples
8. Kernel Density Estimation R Examples