Outliers may hamper proper classical multivariate analysis, and lead to incorrect conclusions. To remedy the problem of outliers, robust methods are developed in statistics and chemometrics. Robust methods reduce or remove the effect of outlying data points and allow the 'good' data to primarily determine the result. This article reviews the most commonly used robust multivariate regression and exploratory methods that have appeared since 1996 in the field of chemometrics. Special emphasis is put on the robust versions of chemometric standard tools like PCA and PLS and the corresponding robust estimates of regression, location and scatter on which they are based.

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Gas chromatograms of fatty acid methyl esters and of volatile lipid oxidation products from fish lipid extracts are analyzed by multivariate data analysis [principal component analysis (PCA)]. Peak alignment is necessary in order to include all sampled points of the chromatograms in the data set. The ability of robust algorithms to deal with outlier problems, including both sample-wise and element-wise outliers, and the advantages and drawbacks of two robust PCA methods, robust PCA (ROBPCA) and robust singular value decomposition when analysing these GC data were investigated. The results show that the usage of ROPCA is advantageous, compared with traditional PCA, when analysing the entire profile of chromatographic data in cases of sub-optimally aligned data. It also demonstrates how choosing the most robust PCA (sample or element-wise) depends on the type of outliers present in the data set.