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

ISBN-13: 9781441904676 / Angielski / Miękka / 2010 / 234 str.

Hannu Oja

Opis

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.

Recenzje

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)

Spis treści

Multivariate location and scatter models.- Location and scatter functionals and sample statistics.- Multivariate signs and ranks.- One-sample problem: 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.

Blurb

This book offers a new, fairly efficient, and robust alternative to analyzing 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 regular L2 norm is just replaced by different L1 norms, observation vectors are replaced by spatial signs and ranks, and so on. A unified methodology starting with the simple one-sample multivariate location problem and proceeding to the general multivariate multiple linear regression case is presented. Companion estimates and tests for scatter matrices are considered as well. The R package MNM is available for computation of the procedures. This monograph provides an up-to-date overview of the theory of multivariate nonparametric methods based on spatial signs and ranks. The classical book by Puri and Sen (1971) uses marginal signs and ranks and different type of L1 norm. The book may serve as a textbook and a general reference for the latest developments in the area. Readers are assumed to have a good knowledge of basic statistical theory as well as matrix theory. Hannu Oja is an academy professor and a professor in biometry in the University of Tampere. He has authored and coauthored numerous research articles in multivariate nonparametrical and robust methods as well as in biostatistics.