On robust partial least squares (PLS) methods

Robust methods for multivariate data analysis

“…Gil and Romera [88], Wakeling and Macfie [85] and Griep et al [86] claimed that substituting all steps of the ordinary LS regression steps in the NIPALS PLS algorithm by a robust regression procedure will make the model completely resistant to outliers, but there are several prices to be paid: Not just a higher computational demand, but also a lower efficiency of the robust steps. Thus, an alternative approach is to replace one or two selected regression steps instead of all steps together which could still show a good performance in terms of handling outliers.…”

“…Thus, an alternative approach is to replace one or two selected regression steps instead of all steps together which could still show a good performance in terms of handling outliers. Such procedures are called semirobust [86,88].…”

“…According to Gil and Romera [88] this way of making the PLS models robust, by substituting some or all regressions steps with a robust alternative, does not necessarily catch 'multivariate' outliers. This is due to the fact that the first step of PLS is not just one regression, but is formed from the individual regressions of each variable x j on y.…”

Influence properties of partial least squares regression

“…as in [14,15], might result in bounded influence functions. Computation of the IF for robust PLS procedures will be presented in a forthcoming article.…”

“…Hence, in the practical applications the IF will always be evaluated for G taken to be Gn . This implies that all quantities s, S, ah, ah, Hh, i3h' rh, ... appearing in (15) or (16) are taken to be the sample estimates as obtained by plugging Gn in the equations (5) or (6).…”