Lecture Notes in Statistics

Multivariate Nonparametric Methods with R

An approach based on spatial signs and ranks

Authors: Oja, Hannu

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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
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  • ISBN 978-1-4419-0468-3
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Softcover $139.99
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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)


Table of contents (14 chapters)

Table of contents (14 chapters)
  • Introduction

    Oja, Prof. Hannu

    Pages 1-4

  • Multivariate location and scatter models

    Oja, Prof. Hannu

    Pages 5-13

  • Location and scatter functionals and sample statistics

    Oja, Prof. Hannu

    Pages 15-27

  • Multivariate signs and ranks

    Oja, Prof. Hannu

    Pages 29-46

  • One-sample problem: Hotelling’s T 2-test

    Oja, Prof. Hannu

    Pages 47-57

Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-1-4419-0468-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $139.99
price for USA in USD
  • ISBN 978-1-4419-0467-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Multivariate Nonparametric Methods with R
Book Subtitle
An approach based on spatial signs and ranks
Authors
Series Title
Lecture Notes in Statistics
Series Volume
199
Copyright
2010
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-1-4419-0468-3
DOI
10.1007/978-1-4419-0468-3
Softcover ISBN
978-1-4419-0467-6
Series ISSN
0930-0325
Edition Number
1
Number of Pages
XIV, 234
Topics