# Asymptotic theory of multiple-set linear canonical analysis

## TL;DR

This paper develops the asymptotic theory for multiple-set linear canonical analysis (MSLCA), including estimators, their properties, and a test for mutual non-correlation among Euclidean random variables.

## Contribution

It introduces a new asymptotic framework for MSLCA, including consistent and asymptotically normal estimators based on empirical covariance operators.

## Key findings

- Proved consistency of MSLCA estimators
- Established asymptotic normality of estimators
- Developed a statistical test for mutual non-correlation

## Abstract

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.