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An Overview of Kriging and Cokriging Predictors for Functional Random Fields

Author

Listed:
  • Ramón Giraldo

    (Departamento de Estadística, Universidad Nacional de Colombia, Sede Bogotá, Bogotá 111321, Colombia)

  • Víctor Leiva

    (School of Industrial Engineering, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362807, Chile)

  • Cecilia Castro

    (Centre of Mathematics, Universidade do Minho, 4710-057 Braga, Portugal)

Abstract

This article presents an overview of methodologies for spatial prediction of functional data, focusing on both stationary and non-stationary conditions. A significant aspect of the functional random fields analysis is evaluating stationarity to characterize the stability of statistical properties across the spatial domain. The article explores methodologies from the literature, providing insights into the challenges and advancements in functional geostatistics. This work is relevant from theoretical and practical perspectives, offering an integrated view of methodologies tailored to the specific stationarity conditions of the functional processes under study. The practical implications of our work span across fields like environmental monitoring, geosciences, and biomedical research. This overview encourages advancements in functional geostatistics, paving the way for the development of innovative techniques for analyzing and predicting spatially correlated functional data. It lays the groundwork for future research, enhancing our understanding of spatial statistics and its applications.

Suggested Citation

  • Ramón Giraldo & Víctor Leiva & Cecilia Castro, 2023. "An Overview of Kriging and Cokriging Predictors for Functional Random Fields," Mathematics, MDPI, vol. 11(15), pages 1-22, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:15:p:3425-:d:1211727
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    References listed on IDEAS

    as
    1. Luis Sánchez & Víctor Leiva & Manuel Galea & Helton Saulo, 2020. "Birnbaum-Saunders Quantile Regression Models with Application to Spatial Data," Mathematics, MDPI, vol. 8(6), pages 1-17, June.
    2. Ramón Giraldo & Luis Herrera & Víctor Leiva, 2020. "Cokriging Prediction Using as Secondary Variable a Functional Random Field with Application in Environmental Pollution," Mathematics, MDPI, vol. 8(8), pages 1-13, August.
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