Theory of Nonparametric Tests

Description

This textbook provides a self-contained presentation of the main concepts and methods of nonparametric statistical testing, with a particular focus on the theoretical foundations of goodness-of-fit tests, rank tests, resampling tests, and projection tests. The substitution principle is employed as a unified approach to the nonparametric test problems discussed. In addition to mathematical theory, it also includes numerous examples and computer implementations. The book is intended for advanced undergraduate, graduate, and postdoc students as well as young researchers. Readers should be familiar with the basic concepts of mathematical statistics typically covered in introductory statistics courses. Front Matter ....Pages i-xii Introduction and Examples (Thorsten Dickhaus)....Pages 1-23 Empirical Measures, Empirical Processes (Thorsten Dickhaus)....Pages 25-35 Goodness-of-Fit Tests (Thorsten Dickhaus)....Pages 37-46 Rank Tests (Thorsten Dickhaus)....Pages 47-69 Asymptotics of Linear Resampling Statistics (Thorsten Dickhaus)....Pages 71-89 Bootstrap Methods for Linear Models (Thorsten Dickhaus)....Pages 91-103 Projection Tests (Thorsten Dickhaus)....Pages 105-118 Some Extensions (Thorsten Dickhaus)....Pages 119-126 Back Matter ....Pages 127-128