An Introduction to Nonparametric Statistics
Kolassa, John E.
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
- Rank-based techniques, including sign, Kruskal-Wallis, Friedman, Mann-Whitney and Wilcoxon tests, are presented.
- Tests are inverted to produce estimates and confidence intervals.
- Multivariate tests are explored.
- Techniques reflecting the dependence of a response variable on explanatory variables are presented.
- Density estimation is explored.
- 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.
John Kolassa is Professor of Statistics and Biostatistics, Rutgers, the State University of New Jersey.