Spatial regression estimation for functional data with spatial dependency

Abstract

We propose a nonparametric estimator of the regression function of a scalar spatial variable Yi given a functional variable Xi. The specificity of the proposed estimator is to depend on two kernels in order to control both the distance between observations and spatial locations. Mean square consistency of this estimator is obtained when the sample considered is an a-mixing sequence. Lastly, numerical results are provided to illustrate the behavior of our estimator.