  We develop a new robust stopping criterion in Partial Least Squares
Regressions (PLSR) components construction characterised by a high level of
stability. This new criterion is defined as a universal one since it is
suitable both for PLSR and its extension to Generalized Linear Regressions
(PLSGLR). This criterion is based on a non-parametric bootstrap process and has
to be computed algorithmically. It allows to test each successive components on
a preset significant level alpha. In order to assess its performances and
robustness with respect to different noise levels, we perform intensive
datasets simulations, with a preset and known number of components to extract,
both in the case n>p (n being the number of subjects and p the number of
original predictors), and for datasets with n<p. We then use t-tests to compare
the performance of our approach to some others classical criteria. The property
of robustness is particularly tested through resampling processes on a real
allelotyping dataset. Our conclusion is that our criterion presents also better
global predictive performances, both in the PLSR and PLSGLR (Logistic and
Poisson) frameworks.
