Fast implementation of partial least squares for function-on-function regression

People employ the function-on-function regression to model relationship between two stochastic processes. Fitting this model, widely used strategies include functional partial least squares algorithms which typically require iterative eigen-decomposition. Here we introduce a route of based upon Krylov subspace. Our can be expressed in forms equivalent each other exact arithmetic: One is non-iterative with explicit expressions estimator and prediction, facilitating theoretical derivation potential extensions; one stabilizes numerical outputs. The consistency estimation prediction established under regularity conditions. It highlighted that our proposal competitive terms both accuracy but consumes much less execution time.