Nonparametric estimation in functional linear model

We consider the problem of estimating the slope parameter in functional linear regression, where scalar responses Y-1, ..., Y-n are modeled in dependence of random functions X-1, ..., X-n. In the case of second order stationary random functions and as well in the non stationary case estimators of the functional slope parameter and its derivatives are constructed based on a regularized inversion of the estimated covariance operator. In this paper the rate of convergence of the estimator is derived assuming that the slope parameter belongs to the well-known Sobolev space of periodic functions and that the covariance operator is finitely, infinitely or in some general form smoothing.