Abstract
A rigorous derivation is provided for canonical correlations and partial canonical correlations for certain Hilbert space indexed stochastic processes. The formulation relies on a key congruence mapping between the space spanned by a second order, $\mathcal{H}$-valued, process and a particular Hilbert function space deriving from the process’ covariance operator. The main results are obtained via an application of methodology for constructing orthogonal direct sums from algebraic direct sums of closed subspaces.
Citation
Qing Huang. Rosemary Renaut. "Functional partial canonical correlation." Bernoulli 21 (2) 1047 - 1066, May 2015. https://doi.org/10.3150/14-BEJ597
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