Robust Multivariate Methods: The Projection Pursuit Approach
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Projection pursuit was originally introduced to identify structures in multivariate data clouds (Huber, 1985). The idea of projecting data to a low-dimensional subspace can also be applied to multivariate statistical methods. The robustness of the methods can be achieved by applying robust estimators to the lower-dimensional space. Robust estimation in high dimensions can thus be avoided which usually results in a faster computation. Moreover, flat data sets where the number of variables is much higher than the number of observations can be easier analyzed in a robust way.
We will focus on the projection pursuit approach for robust continuum regression (Serneels et al., 2005). A new algorithm is introduced and compared with the reference algorithm as well as with classical continuum regression.
KeywordsPartial Little Square Canonical Correlation Analysis Principal Component Regression Projection Direction Robust Estimator
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