An Introduction to Nonparametric Statistics

This textbook presents techniques for statistical analysis in the absence of strong assumptions about the distributions generating the data. Rank-based and resampling techniques are heavily represented, but robust techniques are considered as well. These techniques include one-sample testing and estimation, multi-sample testing and estimation, and regression.

Attention is payed to the intellectual development of the field, with a thorough review of bibliographical references. Computational tools, in R and SAS, are developed and illustrated via examples. Exercises designed to reinforce examples are included.

Important techniques covered include

1. Rank-based techniques, including sign, Kruskal-Wallis, Friedman, Mann-Whitney and Wilcoxon tests, are presented.
2. Tests are inverted to produce estimates and confidence intervals.
3. Multivariate tests are explored.
4. Techniques reflecting the dependence of a response variable on explanatory variables are presented.
5. Density estimation is explored.
6. The bootstrap and jackknife are discussed.

This text is intended for a graduate student in applied statistics. The course is best taken after an introductory course in statistical methodology, a course in elementary probability, and a course in regression. Mathematical prerequisites include calculus through multivariate differentiation and integration, and, ideally, a course in matrix algebra.