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Cokriging Prediction Using as Secondary Variable a Functional Random Field with Application in Environmental Pollution

Author

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  • Ramón Giraldo

    (Department of Statistics, Universidad Nacional de Colombia, Bogotá 111321, Colombia)

  • Luis Herrera

    (Department of Statistics, Universidad Nacional de Colombia, Bogotá 111321, Colombia)

  • Víctor Leiva

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

Abstract

Cokriging is a geostatistical technique that is used for spatial prediction when realizations of a random field are available. If a secondary variable is cross-correlated with the primary variable, both variables may be employed for prediction by means of cokriging. In this work, we propose a predictive model that is based on cokriging when the secondary variable is functional. As in the ordinary cokriging, a co-regionalized linear model is needed in order to estimate the corresponding auto-correlations and cross-correlations. The proposed model is utilized for predicting the environmental pollution of particulate matter when considering wind speed curves as functional secondary variable.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1305-:d:395389
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    References listed on IDEAS

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    1. Henry Velasco & Henry Laniado & Mauricio Toro & Víctor Leiva & Yuhlong Lio, 2020. "Robust Three-Step Regression Based on Comedian and Its Performance in Cell-Wise and Case-Wise Outliers," Mathematics, MDPI, vol. 8(8), pages 1-18, August.
    2. Nerini, David & Monestiez, Pascal & Manté, Claude, 2010. "Cokriging for spatial functional data," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 409-418, February.
    3. Menafoglio, Alessandra & Petris, Giovanni, 2016. "Kriging for Hilbert-space valued random fields: The operatorial point of view," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 84-94.
    4. Helton Saulo & Jeremias Leão & Víctor Leiva & Robert G. Aykroyd, 2019. "Birnbaum–Saunders autoregressive conditional duration models applied to high-frequency financial data," Statistical Papers, Springer, vol. 60(5), pages 1605-1629, October.
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    Cited by:

    1. Alejandra Tapia & Viviana Giampaoli & Víctor Leiva & Yuhlong Lio, 2020. "Data-Influence Analytics in Predictive Models Applied to Asthma Disease," Mathematics, MDPI, vol. 8(9), pages 1-19, September.
    2. 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.
    3. Rodrigo Puentes & Carolina Marchant & Víctor Leiva & Jorge I. Figueroa-Zúñiga & Fabrizio Ruggeri, 2021. "Predicting PM2.5 and PM10 Levels during Critical Episodes Management in Santiago, Chile, with a Bivariate Birnbaum-Saunders Log-Linear Model," Mathematics, MDPI, vol. 9(6), pages 1-24, March.
    4. Jorge I. Figueroa-Zúñiga & Cristian L. Bayes & Víctor Leiva & Shuangzhe Liu, 2022. "Robust beta regression modeling with errors-in-variables: a Bayesian approach and numerical applications," Statistical Papers, Springer, vol. 63(3), pages 919-942, June.
    5. Ghanim Mahmood Dhaher, 2022. "Comparative Evaluation of Prediction Model between Inference Fuzzy System and Universal Kriging for Spatial Data," Technium, Technium Science, vol. 4(1), pages 115-125.
    6. Carlos Martin-Barreiro & John A. Ramirez-Figueroa & Ana B. Nieto-Librero & Víctor Leiva & Ana Martin-Casado & M. Purificación Galindo-Villardón, 2021. "A New Algorithm for Computing Disjoint Orthogonal Components in the Three-Way Tucker Model," Mathematics, MDPI, vol. 9(3), pages 1-22, January.
    7. Pilar García-Soidán & Tomás R. Cotos-Yáñez, 2020. "Use of Correlated Data for Nonparametric Prediction of a Spatial Target Variable," Mathematics, MDPI, vol. 8(11), pages 1-20, November.
    8. Rafael Meléndez & Ramón Giraldo & Víctor Leiva, 2020. "Sign, Wilcoxon and Mann-Whitney Tests for Functional Data: An Approach Based on Random Projections," Mathematics, MDPI, vol. 9(1), pages 1-11, December.

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