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Multivariate Techniques: Robustness

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International Encyclopedia of Statistical Science

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The usual multivariate analysis techniques include location and scatter estimation, principal component analysis, factor analysis (see Factor Analysis and Latent Variable Modelling), discriminant analysis (see Discriminant Analysis: An Overview, and Discriminant Analysis: Issues and Problems), canonical correlation analysis, multiple regression and cluster analysis (see Cluster Analysis: An Introduction). These methods all try to describe and discover structure in the data, and thus rely on the correlation structure between the variables. Classical procedures typically assume normality (i.e. gaussianity) and consequently use the sample mean and sample covariance matrix to estimate the true underlying model parameters.

Below are three examples of multivariate settings used to analyze a data set with n objects and p variables, forming an n ×p data matrix \(X = ({x}_{1},\ldots ,{x}_{n})'\) with \({x}_{i} = ({x}_{i1},\ldots ,{x}_{ip})'\) the ith observation.

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Author information

Authors and Affiliations

  1. Katholieke Universiteit Leuven, Leuven, Belgium

    Mia Hubert (Associate Professor)

  2. Renaissance Technologies, New York, NY, USA

    Peter J. Rousseeuw (Senior Researcher)

Authors
  1. Mia Hubert
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  2. Peter J. Rousseeuw
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Editor information

Editors and Affiliations

  1. Department of Statistics and Informatics, Faculty of Economics, University of Kragujevac, City of Kragujevac, Serbia

    Miodrag Lovric

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Hubert, M., Rousseeuw, P.J. (2011). Multivariate Techniques: Robustness. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_401

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