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When analyzing data, outlying observations cause problems because they may strongly influence the result. Robust statistics aims at detecting the outliers by searching for the model fitted by the majority of the data. We present an overview of several robust methods and outlier detection tools. We discuss robust procedures for univariate, low‐dimensional, and high‐dimensional data such as estimation of location and scatter, linear regression, principal component analysis, and classification. © 2011 John Wiley & Sons, Inc. WIREs Data Mining Knowl Discov 2011 1 73‐79 DOI: 10.1002/widm.2 This article is categorized under: Algorithmic Development > Biological Data Mining Algorithmic Development > Spatial and Temporal Data Mining Application Areas > Health Care Technologies > Structure Discovery and Clustering

Partial least squares regression (PLSR) is a linear regression technique developed to deal with highdimensional regressors and one or several response variables. In this paper we introduce robustified versions of the SIMPLS algorithm, this being the leading PLSR algorithm because of its speed and efficiency. Because SIMPLS is based on the empirical cross-covariance matrix between the response variables and the regressors and on linear least squares regression, the results are affected by abnormal observations in the data set. Two robust methods, RSIMCD and RSIMPLS, are constructed from a robust covariance matrix for high-dimensional data and robust linear regression. We introduce robust RMSECV and RMSEP values for model calibration and model validation. Diagnostic plots are constructed to visualize and classify the outliers. Several simulation results and the analysis of real data sets show the effectiveness and robustness of the new approaches. Because RSIMPLS is roughly twice as fast as RSIMCD, it stands out as the overall best method.

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