On estimation and prediction in spatial functional linear regression model

We consider a spatial functional linear regression, where a scalar response is related to a square-integrable spatial functional process. We use a smoothing spline estimator for the functional slope parameter and establish a finite sample bound for variance of this estimator. Then we give the optimal bound of the prediction error under mixing spatial dependence. Finally, we illustrate our results by simulations and by an application to ozone pollution forecasting at nonvisited sites.