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Revista Colombiana de Estadística
Print version ISSN 0120-1751
Rev.Colomb.Estad. vol.45 no.2 Bogotá July/Dec. 2022 Epub Feb 02, 2023
https://doi.org/10.15446/rce.v45n2.98957
Artículos originales de investigación
Nonparametric Prediction for Spatial Dependent Functional Data Under Fixed Sampling Design
Predicción no paramétrica para datos funcionales dependientes del espacio bajo un diseño de muestreo fijo
1 Higher Polytechnic School (ESP), Cheikh Anta Diop University (UCAD), Dakar, Senegal
2 Department of Mathematics, University of Lille, Villeneuve d'ascq, France
3 Department of Mathematics and Computer Science, Faculty of Sciences and Technologies, Cheikh Anta Diop University, Dakar, Senegal
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.
Key words: Functional dependent data; Fixed design; Non-parametric prediction; Supervised classification
En este trabajo consideramos una predicción no paramétrica de un proceso espacial y funcional observado bajo un diseño de muestreo no aleatorio. El predictor propuesto se basa en la regresión funcional y depende de dos núcleos, uno de los cuales controla la estructura espacial y el otro mide la proximidad entre las observaciones funcionales. Esta metodología puede considerarse, en particular, como una nueva herramienta de clasificación supervisada cuando la variable de interés pertenece a un conjunto finito discreto predefinido. El error cuadrático medio y la convergencia casi completa (o certera) se obtienen cuando la muestra considerada es una a realizado estudios numéricos para ilustrar el comportamiento de nuestro predictor. Esta aplicación mediante simulación de un modelo numérico muestra que el método de predicción propuesto supera al predictor clásico que no tiene en cuenta la estructura espacial.
Palabras clave: Clasificación supervisada; Datos funcionales dependientes; Diseño fijo; Predicción no paramétrica
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Received: November 2021; Accepted: May 2022
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