Multivariate Nonparametric Methods with R

An approach based on spatial signs and ranks

  • Hannu Oja

Part of the Lecture Notes in Statistics book series (LNS, volume 199)

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Hannu Oja
    Pages 1-4
  3. Hannu Oja
    Pages 29-46
  4. Hannu Oja
    Pages 107-129
  5. Hannu Oja
    Pages 131-143
  6. Hannu Oja
    Pages 145-170
  7. Hannu Oja
    Pages 171-182
  8. Hannu Oja
    Pages 183-200
  9. Hannu Oja
    Pages 201-208
  10. Back Matter
    Pages 209-232

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.


Median STATISTICA linear regression multivariate analysis multivariate linear regression scatter matrix spatial signs and ranks statistical computing

Authors and affiliations

  • Hannu Oja
    • 1
  1. 1.University of TampereTAmpereFinland

Bibliographic information