Nonparametric Prediction for Spatial Dependent Functional Data Under Fixed Sampling Design

• Autores: Mamadou Ndiaye, Sophie Dabo-Niang, Papa Ngom
• Localización: Revista Colombiana de Estadística, ISSN-e 2389-8976, ISSN 0120-1751, Vol. 45, Nº. 2, 2022, págs. 391-428
• Idioma: inglés
• DOI: 10.15446/rce.v45n2.98957
• Títulos paralelos:
  • Predicción no paramétrica para datos funcionales dependientes del espacio bajo un diseño de muestreo fijo
• Enlaces
  • Texto completo
• Resumen
  • español

    Resumen 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.

  • English

    Abstract 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.

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