Abstract
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.
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Filzmoser, P., Serneels, S., Croux, C., Van Espen, P.J. (2006). Robust Multivariate Methods: The Projection Pursuit Approach. In: Spiliopoulou, M., Kruse, R., Borgelt, C., Nürnberger, A., Gaul, W. (eds) From Data and Information Analysis to Knowledge Engineering. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-31314-1_32
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DOI: https://doi.org/10.1007/3-540-31314-1_32
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