Hettmansperger T.P., McKean J.W. Robust Nonparametric Statistical Methods

2nd ed. — CRC Press, 2010. — 553 p. — ISB: 1439809089, 9781439809082Presenting an extensive set of tools and methods for data analysis, Robust Nonparametric Statistical Methods, Second Edition covers univariate tests and estimates with extensions to linear models, multivariate models, times series models, experimental designs, and mixed models. It follows the approach of the first edition by developing rank-based methods from the unifying theme of geometry. This edition, however, includes more models and methods and significantly extends the possible analyses based on ranks.New to the Second Edition
A new section on rank procedures for nonlinear models
A new chapter on models with dependent error structure, covering rank methods for mixed models, general estimating equations, and time series
New material on the development of computationally efficient affine invariant/equivariant sign methods based on transform-retransform techniques in multivariate models
Taking a comprehensive, unified approach to statistical analysis, the book continues to describe one- and two-sample problems, the basic development of rank methods in the linear model, and fixed effects experimental designs. It also explores models with dependent error structure and multivariate models. The authors illustrate the implementation of the methods using many real-world examples and R. More information about the data sets and R packages.One-Sample ProblemsLocation Model
Geometry and Inference in the Location Model
Examples
Properties of Norm-Based Inference
Robustness Properties of Norm-Based Inference
Inference and the Wilcoxon Signed-Rank Norm
Inference Based on General Signed-Rank Norms
Ranked Set Sampling
L1 Interpolated Confidence Intervals
Two-Sample Analysis
Two-Sample ProblemsGeometric Motivation
Examples
Inference Based on the Mann-Whitney-Wilcoxon
General Rank Scores
L1 Analyses
Robustness Properties
Proportional Hazards
Two-Sample Rank Set Sampling (RSS)
Two-Sample Scale Problem
Behrens-Fisher Problem
Paired Designs
Linear ModelsGeometry of Estimation and Tests
Examples
Assumptions for Asymptotic Theory
Theory of Rank-Based Estimates
Theory of Rank-Based Tests
Implementation of the R Analysis
L1 Analysis
Diagnostics
Survival Analysis
Correlation Model
High Breakdown (HBR) Estimates
Diagnostics for Differentiating between Fits
Rank-Based Procedures for Nonlinear Models
Experimental Designs: Fixed EffectsOne-Way Design
Multiple Comparison Procedures
Two-Way Crossed Factorial
Analysis of Covariance
Further Examples
Rank Transform
Models with Dependent Error StructureGeneral Mixed Models
Simple Mixed Models
Arnold Transformations
General Estimating Equations (GEE)
Time Series
Multivariate
Multivariate Location Model
Componentwise
Spatial Methods
Affine Equivariant and Invariant Methods
Robustness of Estimates of Location
Linear Model
Experimental DesignsAppendix: Asymptotic Results