Regularized Functional Canonical Correlation Analysis for Stochastic Processes

Abstract: In this paper we derive the asymptotic distributions of two distinct regularized estimators for functional canonical correlation as well as their associated eigenvalues, eigenvectors and projection operators. The methods we developed utilize regularized estimators which approach the functional operators based in reproducing kernel Hilbert spaces (RKHS) as the regularization parameter approaches zero. In addition to providing some justification for the RKHS methods, we explore the asymptotics of regularized operators associated with both Tikhinov and truncated singular value decomposition (TSVD) type regularization. Together, these regularization methods represent two of the most commonly utilized forms of regularization.