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Optimal sampling for spatial prediction of functional data

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  • Martha Bohorquez
  • Ramón Giraldo
  • Jorge Mateu

Abstract

This paper combines optimal spatial sampling designs with geostatistical analysis of functional data. We propose a methodology and design criteria to find the set of spatial locations that minimizes the variance of the spatial functional prediction at unsampled sites for three functional predictors: ordinary kriging, simple kriging and simple cokriging. The last one is a modification of an existing predictor that uses ordinary cokriging based on the basis coefficients. Instead, we propose to use a simple cokriging predictor with the scores resulting from a representation of the functional data with the empirical functional principal components, allowing to remove restrictions and complexity of the covariance models and constraints on the estimation procedure. The methodology is applied to a network of air quality in Bogotá city, Colombia. Copyright Springer-Verlag Berlin Heidelberg 2016

Suggested Citation

  • Martha Bohorquez & Ramón Giraldo & Jorge Mateu, 2016. "Optimal sampling for spatial prediction of functional data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(1), pages 39-54, March.
    • Handle: RePEc:spr:stmapp:v:25:y:2016:i:1:p:39-54
    DOI: 10.1007/s10260-015-0340-9
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    References listed on IDEAS

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    1. Piercesare Secchi & Simone Vantini & Valeria Vitelli, 2015. "Rejoinder to the discussion of “Analysis of Spatio-Temporal Mobile Phone Data: a Case Study in the Metropolitan Area of Milan”," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(2), pages 335-338, July.
    2. Caselton, W. F. & Zidek, J. V., 1984. "Optimal monitoring network designs," Statistics & Probability Letters, Elsevier, vol. 2(4), pages 223-227, August.
    3. Piercesare Secchi & Simone Vantini & Valeria Vitelli, 2015. "Analysis of spatio-temporal mobile phone data: a case study in the metropolitan area of Milan," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(2), pages 279-300, July.
    4. Mia Hubert & Peter Rousseeuw & Pieter Segaert, 2015. "Multivariate functional outlier detection," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(2), pages 177-202, July.
    5. Nerini, David & Monestiez, Pascal & Manté, Claude, 2010. "Cokriging for spatial functional data," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 409-418, February.
    6. Mia Hubert & Peter Rousseeuw & Pieter Segaert, 2015. "Rejoinder to ‘multivariate functional outlier detection’," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(2), pages 269-277, July.
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    Cited by:

    1. Roberto Benedetti & Federica Piersimoni & Paolo Postiglione, 2017. "Spatially Balanced Sampling: A Review and A Reappraisal," International Statistical Review, International Statistical Institute, vol. 85(3), pages 439-454, December.
    2. Giraldo, Ramón & Dabo-Niang, Sophie & Martínez, Sergio, 2018. "Statistical modeling of spatial big data: An approach from a functional data analysis perspective," Statistics & Probability Letters, Elsevier, vol. 136(C), pages 126-129.
    3. Yu-ting Bai & Xue-bo Jin & Xiao-yi Wang & Xiao-kai Wang & Ji-ping Xu, 2020. "Dynamic Correlation Analysis Method of Air Pollutants in Spatio-Temporal Analysis," IJERPH, MDPI, vol. 17(1), pages 1-19, January.

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