# On estimation and prediction in spatial functional linear regression model

## TL;DR

This paper develops a smoothing spline estimator for spatial functional linear regression, providing finite sample bounds for variance and prediction error, supported by simulation studies.

## Contribution

It introduces a novel estimator for the spatial functional linear model and derives finite sample bounds under spatial dependence.

## Key findings

- Finite sample variance bounds for the estimator.
- Prediction error bounds established.
- Simulation results validate theoretical findings.

## Abstract

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 under mixing spatial dependence. Then, we give a bound of the prediction error. Finally, we illustrate our results by simulations