  By deriving influence functions related to multiple-set linear canonical
analysis (MSLCA) we show that the classical version of this analysis, based on
empirical covariance operators, is not robust. Then, we introduce a robust
version of MSLCA by using the MCD estimator of the covariance operator of the
involved random vector. The related influence functions are then derived and
are shown to be bounded. Asymptotic properties of the introduced robust MSLCA
are obtained and permit to propose a robust test for mutual non-correlation.
This test is shown to be robust by studying the related second order influence
function under the null hypothesis.
