Spatial regression estimation for functional data with spatial dependency

Ternynck, Camille

Journal de la société française de statistique, Tome 155 (2014) no. 2, pp. 138-160.

Nous proposons un estimateur non paramétrique de la fonction de régression d’une variable spatiale, $Y_{\mathbf{i}}$, scalaire conditionnellement à une variable, $X_{\mathbf{i}}$, fonctionnelle. La spécificité de l’estimateur proposé est de dépendre de deux noyaux permettant de contrôler à la fois la distance entre les observations et les sites. La convergence en moyenne quadratique de cet estimateur est obtenue quand l’échantillon considéré est une séquence $\alpha$-mélangeante. Pour terminer, des résultats numériques illustrent le comportement de notre estimateur.

We propose a nonparametric estimator of the regression function of a scalar spatial variable $Y_{\mathbf{i}}$ given a functional variable $X_{\mathbf{i}}$. 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 $\alpha$-mixing sequence. Lastly, numerical results are provided to illustrate the behavior of our estimator.

Keywords: kernel regression estimation, spatial process, functional data
Mot clés : estimation à noyau de la régression, processus spatial, données fonctionnelles

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