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By deriving influence functions related to multiple-set linear canonicalanalysis (MSLCA) we show that the classical version of this analysis, based onempirical covariance operators, is not robust. Then, we introduce a robustversion of MSLCA by using the MCD estimator of the covariance operator of theinvolved random vector. The related influence functions are then derived andare shown to be bounded. Asymptotic properties of the introduced robust MSLCAare 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 influencefunction under the null hypothesis.

Robust multiple-set linear canonical analysis based on minimum covariance determinant estimator