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Robust Multivariate Analysis

  • Textbook
  • © 2017

Overview

Authors:
  1. David J. Olive

    1. Department of Mathematics, Southern Illinois University, Carbondale, USA

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  • Includes dozens of R functions for making plots and estimators

  • Problems included at the end of every chapter

  • Code available for download on the author's website

  • Includes supplementary material: sn.pub/extras

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-xvi
    Download chapter PDF

  2. Introduction

    • David J. Olive
    Pages 1-23

  3. Multivariate Distributions

    • David J. Olive
    Pages 25-46

  4. Elliptically Contoured Distributions

    • David J. Olive
    Pages 47-85

  5. MLD Estimators

    • David J. Olive
    Pages 87-137

  6. DD Plots and Prediction Regions

    • David J. Olive
    Pages 139-188

  7. Principal Component Analysis

    • David J. Olive
    Pages 189-217

  8. Canonical Correlation Analysis

    • David J. Olive
    Pages 219-231

  9. Discriminant Analysis

    • David J. Olive
    Pages 233-272

  10. Hotelling’s \(T^2\) Test

    • David J. Olive
    Pages 273-289

  11. MANOVA

    • David J. Olive
    Pages 291-310

  12. Factor Analysis

    • David J. Olive
    Pages 311-326

  13. Multivariate Linear Regression

    • David J. Olive
    Pages 327-384

  14. Clustering

    • David J. Olive
    Pages 385-391

  15. Other Techniques

    • David J. Olive
    Pages 393-459

  16. Stuff for Students

    • David J. Olive
    Pages 461-477

  17. Back Matter

    Pages 479-501
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Keywords

About this book

This text presents methods that are robust to the assumption of a multivariate normal distribution or methods that are robust to certain types of outliers. Instead of using exact theory based on the multivariate normal distribution, the simpler and more applicable large sample theory is given.  The text develops among the first practical robust regression and robust multivariate location and dispersion estimators backed by theory.  

The robust techniques  are illustrated for methods such as principal component analysis, canonical correlation analysis, and factor analysis.  A simple way to bootstrap confidence regions is also provided.

Much of the research on robust multivariate analysis in this book is being published for the first time.  The text is suitable for a first course in Multivariate Statistical Analysis or a first course in Robust Statistics.  This graduate text is also useful for people who are familiar with the traditional multivariate topics, but want to know more about handling data sets with outliers. Many R programs and R data sets are available on the author’s website. 

Reviews

“This monograph provides a comprehensive introduction to the mathematical theory of framelets and discrete framelet transforms. … This monograph is well-written for a broad readership and very convenient as a textbook for graduate students and as an advanced reference guide for researchers in applied mathematics, physics, and engineering. Doubtless, this work will stimulate further research on framelets.” (Manfred Tasche, zbMATH 1387.42001, 2018)

Authors and Affiliations

  • Department of Mathematics, Southern Illinois University, Carbondale, USA

    David J. Olive

About the author

David Olive is a Professor at Southern Illinois University, Carbondale, IL, USA.  His research interests include the development of computationally practical robust multivariate location and dispersion estimators, robust multiple linear regression estimators, and resistant dimension reduction estimators. 

Bibliographic Information

  • Book Title: Robust Multivariate Analysis

  • Authors: David J. Olive

  • DOI: https://doi.org/10.1007/978-3-319-68253-2

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing AG 2017

  • Hardcover ISBN: 978-3-319-68251-8Published: 13 December 2017

  • Softcover ISBN: 978-3-319-88571-1Published: 23 May 2018

  • eBook ISBN: 978-3-319-68253-2Published: 28 November 2017

  • Edition Number: 1

  • Number of Pages: XVI, 501

  • Number of Illustrations: 70 b/w illustrations, 6 illustrations in colour

  • Topics: Probability Theory and Stochastic Processes, Statistical Theory and Methods

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