  When applying a statistical method in practice it often occurs that some
observations deviate from the usual assumptions. However, many classical
methods are sensitive to outliers. The goal of robust statistics is to develop
methods that are robust against the possibility that one or several unannounced
outliers may occur anywhere in the data. These methods then allow to detect
outlying observations by their residuals from a robust fit. We focus on
high-breakdown methods, which can deal with a substantial fraction of outliers
in the data. We give an overview of recent high-breakdown robust methods for
multivariate settings such as covariance estimation, multiple and multivariate
regression, discriminant analysis, principal components and multivariate
calibration.
