Canonical correlation analysis of functional data
King, David · ProQuest Demo Repository
The most general framework for canonical correlation analysis between two second order stochastic processes is based on the singular value decomposition of a certain operator defined on the reproducing kernel Hilbert spaces associated with the covariance kernels of the processes. Computations using this operator require the solution of inverse problems involving compact operators. As a result, regularization methods are needed to ensure effective computation of both canonical correlations and variables. In this regard, both the Tikhinov and truncated singular value decomposition methods are shown to produce regularized canonical correlations and variables that converge to the optimal solutions under suitable behavior for their respective regularization parameters. Sample analogs of the regularization operators are considered and their associated asymptotic distribution theory is developed. As part of a theoretical overview a new isometry is obtained that connects the orthogonal complement of the null space of the covariance operator to the Hilbert space spanned by the stochastic process.