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 is 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.

中文翻译：

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多集线性典范分析的渐近理论

本文讨论了用于多集线性规范分析（MSLCA）的渐近性。给出了该分析的定义，该定义使经典的分析适合于欧几里得随机变量的上下文，并推导了相关规范系数的性质。然后，提出了基于经验协方差算子的MSLCA元素的估计量，并获得了这些估计量的渐近性。更准确地说，我们证明了它们的一致性，并且获得了给出MSLCA的算子的估计量以及规范系数向量的估计量的渐近正态性。然后将这些结果用于获得所涉及的欧几里得随机变量之间互不相关的检验。