Robust Multivariate Analysis

1. Front Matter

   Pages i-xvi

   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

    PDF

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. 

• Robust Statistics
• Prediction Region
• Bootstrap Confidence Region
• Multivariate Regression
• Principal Component Analysis
• Canonical Correlation Analysis
• Discriminant Analysis
• MANOVA

“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)

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

  David J. Olive

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. 

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