Robust Multivariate Analysis

ISBN-13: 9783319682518 / Angielski / Twarda / 2017 / 501 str.

David Olive

Opis

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. The robust techniques are illustrated for methods such as principal component analysis, canonical correlation analysis, and factor analysis.

Recenzje

"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)

Spis treści

Introduction.- Multivariate Distributions.- Elliptically Contoured Distributions.- MLD Estimators.- DD Plots and Prediction Regions.- Principal Component Analysis.- Canonical Correlation Analysis.- Discrimination Analysis.- Hotelling's T^2 Test.- MANOVA.- Factor Analysis.- Multivariate Linear Regression.- Clustering.- Other Techniques.- Stuff for Students.

O autorze

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. 

Blurb

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.