This book introduces a new way to analyze multivariate data. The analysis of data based on multivariate spatial signs and ranks proceeds very much as does a tra- tional multivariate analysis relying on the assumption of multivariate normality: the L norm is just replaced by different L norms, observation vectors are replaced by 2 1 their(standardizedandcentered)spatial signsandranks, andso on.Themethodsare fairly ef?cient and robust, and no moment assumptions are needed. A uni?ed t- ory starting with the simple one-sample location problem and proceeding through the several-sample location problems to the general multivariate linear regression model and ?nally to the analysis of cluster-dependent data is presented. The material is divided into 14 chapters. Chapter 1 serves as a short introd- tion to the general ideas and strategies followed in the book. Chapter 2 introduces and discusses different types of parametric, nonparametric, and semiparametric s- tistical models used to analyze the multivariate data. Chapter 3 provides general descriptive tools to describe the properties of multivariate distributions and mul- variate datasets. Multivariate location and scatter functionals and statistics and their use is described in detail. Chapter 4 introduces the concepts of multivariate spatial sign, signed-rank, andrank, and shows their connectionto certain L objectivefunc- 1 tions. Also sign and rank covariance matrices are discussed carefully. The ?rst four chapters thus provide the necessary tools to understand the remaining part of the book.
From the reviews:
"This monograph, part of the Lecture Notes in Statistics series, provides a complete overview of multivariate analysis methods based on spatial signs and ranks. It covers a wide range of topics in classical multivariate analysis and presents some deep theoretical results. ... It may serve as 'a general reference for the latest developments in the area.' ... In summary, Multivariate Nonparametric Methods With R is a good reference book for the area of multivariate nonparametric methods based on spatial signs and ranks ... ." (Gang Shen, Journal of the American Statistical Association, Vol. 106 (496), December, 2011)
"This book provides an overview of the theory of multivariate nonparametric methods based on spatial signs and ranks. ... In most chapters, the theory and methods are illustrated with examples. Furthermore, the R package MNM is available for computation of the procedures, and the code for the analysis of example data set is also provided in the text." (Elvan Ceyhan, Mathematical Reviews, Issue 2011 g)
Introduction.- Multivariate location and scatter models.- Location and scatter functionals and sample statistics.- Multivariate signs and ranks.- One-sample problems: Hotelling's T2-test.- One-sample problem: Spatial sign test and spatial median.- One-sample problem: Spatial signed-rank test and Hodges-Lehmann estimate.- One-sample problem: Comparisons of tests and estimates.- One-sample problem: Inference for shape.- Multivariate tests of independence.- Several-sample location problem.- Randomized blocks.- Multivariate linear regression.- Analysis of cluster-correlated data.