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Mantel test for spatial functional data

Author

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  • Ramón Giraldo

    (Universidad Nacional de Colombia)

  • William Caballero

    (Escuela Naval de Cadetes)

  • Jesús Camacho-Tamayo

    (Universidad Nacional de Colombia)

Abstract

Statistics for spatial functional data is an emerging field in statistics which combines methods of spatial statistics and functional data analysis to model spatially correlated functional data. Checking for spatial autocorrelation is an important step in the statistical analysis of spatial data. Several statistics to achieve this goal have been proposed. The test based on the Mantel statistic is widely known and used in this context. This paper proposes an application of this test to the case of spatial functional data. Although we focus particularly on geostatistical functional data, that is functional data observed in a region with spatial continuity, the test proposed can also be applied with functional data which can be measured on a discrete set of areas of a region (areal functional data) by defining properly the distance between the areas. Based on two simulation studies, we show that the proposed test has a good performance. We illustrate the methodology by applying it to an agronomic data set.

Suggested Citation

  • Ramón Giraldo & William Caballero & Jesús Camacho-Tamayo, 2018. "Mantel test for spatial functional data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(1), pages 21-39, January.
    • Handle: RePEc:spr:alstar:v:102:y:2018:i:1:d:10.1007_s10182-016-0280-1
    DOI: 10.1007/s10182-016-0280-1
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    References listed on IDEAS

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    1. Elvira Romano & Jorge Mateu & Ramon Giraldo, 2015. "On the performance of two clustering methods for spatial functional data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(4), pages 467-492, October.
    2. Maria Ruiz-Medina & Rosa Espejo & Elvira Romano, 2014. "Spatial functional normal mixed effect approach for curve classification," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(3), pages 257-285, September.
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    5. Berrendero, J.R. & Justel, A. & Svarc, M., 2011. "Principal components for multivariate functional data," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2619-2634, September.
    6. Veerabhadran Baladandayuthapani & Bani K. Mallick & Mee Young Hong & Joanne R. Lupton & Nancy D. Turner & Raymond J. Carroll, 2008. "Bayesian Hierarchical Spatially Correlated Functional Data Analysis with Application to Colon Carcinogenesis," Biometrics, The International Biometric Society, vol. 64(1), pages 64-73, March.
    7. R. Giraldo & P. Delicado & J. Mateu, 2012. "Hierarchical clustering of spatially correlated functional data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 66(4), pages 403-421, November.
    8. C. Comas & P. Delicado & J. Mateu, 2011. "A second order approach to analyse spatial point patterns with functional marks," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 503-523, November.
    9. Dray, Stéphane & Dufour, Anne-Béatrice, 2007. "The ade4 Package: Implementing the Duality Diagram for Ecologists," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 22(i04).
    10. Serge Guillas & Ming-Jun Lai, 2010. "Bivariate splines for spatial functional regression models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(4), pages 477-497.
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    2. Łukasz Smaga, 2020. "A note on repeated measures analysis for functional data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(1), pages 117-139, March.

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