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.