Robust Statistics, 2nd Edition

6Multivariate Analysis

6.1 Introduction

Multivariate analysis deals with situations in which several variables are measured on each experimental unit. In most cases of interest it is known or assumed that some form of relationship exists among the variables, and hence that considering each of them separately would entail a loss of information. Some possible goals of the analysis are:

• reduction of dimensionality (principal components, factor analysis, canonical correlation);
• identification (discriminant analysis);
• explanatory models (multivariate linear model).

The reader is referred to Seber (1984) and Johnson and Wichern (1998) for further details.

A ‐variate observation is now a vector , and a distribution now means a distribution on . In the classical approach, location of a ‐variate random variable is described by the expectation , and scatter is described by the covariance matrix ...