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.

中文翻译：

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空间函数线性回归模型的估计与预测

我们考虑空间函数线性回归，其中标量响应与平方可积空间函数过程相关。我们对函数斜率参数使用平滑样条估计器，并为该估计器的方差建立有限样本界限。然后我们给出了混合空间相关性下预测误差的最优界限。最后，我们通过模拟和未访问地点臭氧污染预测的应用来说明我们的结果。