Test of independence for Hilbertian random variables

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Research Article

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In this article, we propose a test of independence for functional random variables modelled as elements of Hilbert spaces. First, we provide a general recipe for constructing measures of dependence among multiple random functions. These measures are non-negative, and under fairly general assumptions, they take the value zero only when the functions are independent. We consider one such measure based on the d-variable Hilbert-Schmidt Independence Criterion and propose a consistent estimator of this measure. Next, we construct a test for independence based on this estimator and establish its large sample consistency under general alternatives. Extensive simulation studies are carried out to compare the performance of the proposed test with some popular tests available in the literature.



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