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Multivariate Nonparametric Methods with R

An approach based on spatial signs and ranks

  • Book
  • © 2010

Overview

Authors:
  1. Hannu Oja

    1. University of Tampere, TAmpere, Finland

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  • Offers an up-to-date review of of the theory of multivariate
  • nonparametric methods based on spatial signs and ranks
  • Provides concise and self-contained treatment of the theory
  • Examples accompanied by a free R package called MNM allows for
  • immediate experimentation of the procedures

Part of the book series: Lecture Notes in Statistics (LNS)

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Table of contents (14 chapters)

  1. Front Matter

    Pages I-XIII
    Download chapter PDF

  2. Introduction

    • Hannu Oja
    Pages 1-4

  3. Multivariate location and scatter models

    • Hannu Oja
    Pages 5-13

  4. Location and scatter functionals and sample statistics

    • Hannu Oja
    Pages 15-27

  5. Multivariate signs and ranks

    • Hannu Oja
    Pages 29-46

  6. One-sample problem: Hotelling’s T 2-test

    • Hannu Oja
    Pages 47-57

  7. One-sample problem: Spatial sign test and spatial median

    • Hannu Oja
    Pages 59-81

  8. One-sample problem: Spatial signed-rank test and Hodges-Lehmann estimate

    • Hannu Oja
    Pages 83-94

  9. One-sample problem: Comparisons of tests and estimates

    • Hannu Oja
    Pages 95-105

  10. One-sample problem: Inference for shape

    • Hannu Oja
    Pages 107-129

  11. Multivariate tests of independence

    • Hannu Oja
    Pages 131-143

  12. Several-sample location problem

    • Hannu Oja
    Pages 145-170

  13. Randomized blocks

    • Hannu Oja
    Pages 171-182

  14. Multivariate linear regression

    • Hannu Oja
    Pages 183-200

  15. Analysis of cluster-correlated data

    • Hannu Oja
    Pages 201-208

  16. Back Matter

    Pages 209-232
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Keywords

About this book

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.

Reviews

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)

Authors and Affiliations

  • University of Tampere, TAmpere, Finland

    Hannu Oja

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