Bernoulli

  • Bernoulli
  • Volume 21, Number 2 (2015), 1047-1066.

Functional partial canonical correlation

Qing Huang and Rosemary Renaut

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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.

Article information

Source
Bernoulli, Volume 21, Number 2 (2015), 1047-1066.

Dates
First available in Project Euclid: 21 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.bj/1429624970

Digital Object Identifier
doi:10.3150/14-BEJ597

Mathematical Reviews number (MathSciNet)
MR3338656

Zentralblatt MATH identifier
1359.62211

Keywords
congruent Hilbert space covariance operator Hilbert space indexed process orthogonal direct sum

Citation

Huang, Qing; Renaut, Rosemary. Functional partial canonical correlation. Bernoulli 21 (2015), no. 2, 1047--1066. doi:10.3150/14-BEJ597. https://projecteuclid.org/euclid.bj/1429624970


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