  This paper deals with asymptotics for multiple-set linear canonical analysis
(MSLCA). A definition of this analysis, that adapts the classical one to the
context of Euclidean random variables, is given and properties of the related
canonical coefficients are derived. Then, estimators of the MSLCA's elements,
based on empirical covariance operators, are proposed and asymptotics for these
estimators are obtained. More precisely, we prove their consistency and we
obtain asymptotic normality for the estimator of the operator that gives MSLCA,
and also for the estimator of the vector of canonical coefficients. These
results are then used to obtain a test for mutual non-correlation between the
involved Euclidean random variables.
