Abstract
Abstract In this chapter, foundations of robust statistics are introduced, including classic and robust estimators as well as their statistical properties (breakdown point, efficiency, influence function and equivariance property). Then, some robust methods that have gained popularity in recent years are presented. The major benefit of using robust methods stems from the fact that they help providing stable estimates for data containing outliers (food samples that have considerably different compositions in comparison with the majority of samples). Regardless of reasons for their uniqueness, outliers strongly affect data interpretation when any method with the least-squares cost function is used. Therefore, robust methods are more suitable to explore and model data containing natural samples when outliers are expected. In addition to exploration and modeling of multivariate data, processing of incomplete multivariate data that contain outliers is also discussed.
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