Oja H. Multivariate Nonparametric Methods with R: An Approach Based on Spatial Signs and Ranks

Oja H. Multivariate Nonparametric Methods with R: An Approach Based on Spatial Signs and RanksSpringer – 2010, 232 pages
ISBN: 1441904670This 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 traditional multivariate analysis relying on the assumption of multivariate normality: the L2 norm is just replaced by different L1 norms, observation vectors are replaced by their (standardized and centered) spatial signs and ranks, and so on. Themethods are fairly efficient and robust, and no moment assumptions are needed. A unified theory starting with the simple one-sample location problem and proceeding through the several-sample location problems to the general multivariate linear regression model and finally to the analysis of cluster-dependent data is presented.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