  Partial least squares (PLS) is a dimensionality reduction technique used as
an alternative to ordinary least squares (OLS) in situations where the data is
colinear or high dimensional. Both PLS and OLS provide mean based estimates,
which are extremely sensitive to the presence of outliers or heavy tailed
distributions. In contrast, quantile regression is an alternative to OLS that
computes robust quantile based estimates. In this work, the multivariate PLS is
extended to the quantile regression framework, obtaining a theoretical
formulation of the problem and a robust dimensionality reduction technique that
we call fast partial quantile regression (fPQR), that provides quantile based
estimates. An efficient implementation of fPQR is also derived, and its
performance is studied through simulation experiments and the chemometrics well
known biscuit dough dataset, a real high dimensional example.
