Abstract

NDIAYE, Mamadou; DABO-NIANG, Sophie  and  NGOM, Papa. Nonparametric Prediction for Spatial Dependent Functional Data Under Fixed Sampling Design. Rev.Colomb.Estad. [online]. 2022, vol.45, n.2, pp.391-428.  Epub Feb 02, 2023. ISSN 0120-1751.  https://doi.org/10.15446/rce.v45n2.98957.

In this work, we consider a nonparametric prediction of a spatio-functional process observed under a non-random sampling design. The proposed predictor is based on functional regression and depends on two kernels, one of which controls the spatial structure and the other measures the proximity between the functional observations. It can be considered, in particular, as a supervised classification method when the variable of interest belongs to a predefined discrete finite set. The mean square error and almost complete (or sure) convergence are obtained when the sample considered is a locally stationary a-mixture sequence. Numerical studies were performed to illustrate the behavior of the proposed predictor. The finite sample properties based on simulated data show that the proposed prediction method outperforms the cl 1 predictor which not taking into account the spatial structure.

Keywords : Functional dependent data; Fixed design; Non-parametric prediction; Supervised classification.

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