Publication: A robust partial least squares method with applications
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2007-03
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Abstract
Partial least squares regression (PLS) is a linear regression technique developed to relate many
regressors to one or several response variables. Robust methods are introduced to reduce or
remove the effect of outlying data points. In this paper we show that if the sample covariance
matrix is properly robustified further robustification of the linear regression steps of the PLS
algorithm becomes unnecessary. The robust estimate of the covariance matrix is computed by
searching for outliers in univariate projections of the data on a combination of random directions
(Stahel-Donoho) and specific directions obtained by maximizing and minimizing the kurtosis
coefficient of the projected data, as proposed by Peña and Prieto (2006). It is shown that this
procedure is fast to apply and provides better results than other procedures proposed in the
literature. Its performance is illustrated by Monte Carlo and by an example, where the algorithm is
able to show features of the data which were undetected by previous methods.
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Keywords
Kurtosis, Projections, Robust covariance matrix, Stahel-Donoho estimator