LAUSR

Abstract Functional canonical correlation analysis (FCCA) has been applied in many contexts, but the asymptotic properties have not yet been studied enough. In this paper we consider a general setup resembling that of Eubank and Hsing (2008). We focus on the convergence of estimates of the associated canonical functions to their population counterparts. A regularized estimator is proposed based on the Tikhinov regularized approach. Under some conditions, an upper bound is derived for this estimator and furthermore, a sharp lower bound is established. Consequently, the minimax optimal rate is obtained and depends on the level of dependence between the two stochastic processes. A simple simulation is performed to illustrate our methods.