Published

2019-01-01

Some Recent Developments in Inference for Geostatistical Functional Data

Algunos desarrollos recientes en inferencia para datos funcionales geoestadísticos

DOI:

https://doi.org/10.15446/rce.v42n1.77058

Keywords:

Functional data, Spatial statistics (en)
Datos funcionales, Estadística espacial (es)

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Authors

  • Piotr Kokoszka Department of Statistics, Colorado State University, Fort Collins, USA
  • Matthew Reimherr 2Department of Statistics, Penn State University, State College, USA

We review recent developments related to inference
for functions defined at spatial locations. We also consider
time series of functions defined at irregularly distributed
spatial points or on a grid. We focus on kriging, estimation
of the functional mean and principal components, and significance
testing, giving special attention to testing spatio--temporal
separability in the context of functional data. We also highlight
some ideas related to extreme value theory for spatially indexed functional
time series.

Revisamos desarrollos recientes relacionados con la inferencia de funciones definidas en locaciones espaciales. También consideramos series de tiempo funcionales definidas en puntos espaciales irregularmente distribuidos ó en una cuadrícula. Nos centramos en el kriging, la estimación de la media funcional y de los componentes principales, y en la prueba de significancia, dando especial atención a pruebas de separabilidad de espacio-tiempo en el contexto de datos funcionales. También destacamos algunas ideas relaciones con la teoría de valores extremos para series de tiempo funcionales indexadas en el espacio.

References

Aston, J., Pigoli, D. & Tavakoli, S. (2016), ‘Tests for separability in nonparametric covariance operators of random surfaces’, The Annals of Statistics 6, 1906–1948.

Beirlant, J., Goegebeur, Y., Segers, J. & Teugels, J. (2006), Statistics of Extremes: Theory and Applications, John Wiley & Sons.

Caballero, W., Giraldo, R. & Mateu, J. (2013), ‘A universal kriging approach for spatial functional data’, Stochastic Environmental Research and Risk Assessment 27, 1553–1563.

Constantinou, P., Kokoszka, P. & Reimherr, M. (2017), ‘Testing separability of space-time functional processes’, Biometrika 104, 425–437.

Csörgő, M. & Horváth, L. (1997), Limit Theorems in Change-Point Analysis,

Wiley.

Delicado, P., Giraldo, R., Comas, C. & Mateu, J. (2010), ‘Statistics for spatial

functional data: some recent contributions’, Environmetrics 21, 224–239.

French, J., Kokoszka, P., Stoev, S. & Hall, L. (2019), ‘Quantifying the risk of

heat waves using extreme value theory and spatio-temporal functional data’, Computational Statistics and Data Analysis 131, 176–193.

Gelfand, A. E., Diggle, P. J., Fuentes, M. & Guttorp, P., eds (2010), Handbook of Spatial Statistics, CRC Press.

Gromenko, O. & Kokoszka, P. (2012), ‘Testing the equality of mean functions of spatially distributed curves’, Journal of the Royal Statistical Society (C) 61, 715–731.

Gromenko, O. & Kokoszka, P. (2013), ‘Nonparametric inference in small data sets of spatially indexed curves with application to ionospheric trend determination’, Computational Statistics and Data Analysis 59, 82–94.

Gromenko, O., Kokoszka, P. & Reimherr, M. (2017), ‘Detection of change in the spatiotemporal mean function’, Journal of the Royal Statistical Society (B) 79, 29–50.

Gromenko, O., Kokoszka, P. & Sojka, J. (2017), ‘Evaluation of the global cooling trend in the ionosphere using functional regression models with incomplete curves’, The Annals of Applied Statistics 11.

Gromenko, O., Kokoszka, P., Zhu, L. & Sojka, J. (2012), ‘Estimation and testing for spatially indexed curves with application to ionospheric and magnetic field trends’, The Annals of Applied Statistics 6, 669–696.

Hörmann, S. & Kokoszka, P. (2013), ‘Consistency of the mean and the principal components of spatially distributed functional data’, Bernoulli 19, 1535–1558.

Horváth, L. & Kokoszka, P. (2012), Inference for Functional Data with Applications, Springer.

Kokoszka, P. & Reimherr, M. (2017), Introduction to Functional Data Analysis, CRC Press.

Liu, C., Ray, S. & Hooker, G. (2017), ‘Functional principal components analysis of spatially correlated data’, Statistics and Computing 27, 1639–1654.

Lu, N. & Zimmerman, D. (2005), ‘The likelihood ratio test for a separable covariance matrix’, Statistics & Probability Letters 73, 449–457.

Menafoglio, A., Secchi, P. & Rosa, M. D. (2013), ‘A universal kriging predictor for spatially dependent functional data of a hilbert space’, Electronic Journal of Statistics 7, 2209–2240.

Mitchell, M. W., Genton, M. G. & Gumpertz, M. L. (2006), ‘A likelihood ratio test for separability of covariances’, Journal of Multivariate Analysis 97, 1025–1043.

Rishbeth, H. (1990), ‘A greenhouse effect in the ionosphere?’, Planetary and Space Science 38, 945–948.

Roble, R. G. & Dickinson, R. E. (1989), ‘How will changes in carbon dioxide and methane modify the mean structure of the mesosphere and thermosphere?’, 16, 1441–1444.

Schabenberger, O. & Gotway, C. A. (2005), Statistical Methods for Spatial Data Analysis, Chapman & Hall/CRC.

Sherman, M. (2011), Spatial Statistics and Spatio–Temporal Data: Covariance Functions and Directional Properties, Wiley.

Wackernagel, H. (2003), Multivariate Geostatistics, Springer.

How to Cite

APA

Kokoszka, P. & Reimherr, M. (2019). Some Recent Developments in Inference for Geostatistical Functional Data. Revista Colombiana de Estadística, 42(1), 101–122. https://doi.org/10.15446/rce.v42n1.77058

ACM

[1]
Kokoszka, P. and Reimherr, M. 2019. Some Recent Developments in Inference for Geostatistical Functional Data. Revista Colombiana de Estadística. 42, 1 (Jan. 2019), 101–122. DOI:https://doi.org/10.15446/rce.v42n1.77058.

ACS

(1)
Kokoszka, P.; Reimherr, M. Some Recent Developments in Inference for Geostatistical Functional Data. Rev. colomb. estad. 2019, 42, 101-122.

ABNT

KOKOSZKA, P.; REIMHERR, M. Some Recent Developments in Inference for Geostatistical Functional Data. Revista Colombiana de Estadística, [S. l.], v. 42, n. 1, p. 101–122, 2019. DOI: 10.15446/rce.v42n1.77058. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/77058. Acesso em: 13 nov. 2025.

Chicago

Kokoszka, Piotr, and Matthew Reimherr. 2019. “Some Recent Developments in Inference for Geostatistical Functional Data”. Revista Colombiana De Estadística 42 (1):101-22. https://doi.org/10.15446/rce.v42n1.77058.

Harvard

Kokoszka, P. and Reimherr, M. (2019) “Some Recent Developments in Inference for Geostatistical Functional Data”, Revista Colombiana de Estadística, 42(1), pp. 101–122. doi: 10.15446/rce.v42n1.77058.

IEEE

[1]
P. Kokoszka and M. Reimherr, “Some Recent Developments in Inference for Geostatistical Functional Data”, Rev. colomb. estad., vol. 42, no. 1, pp. 101–122, Jan. 2019.

MLA

Kokoszka, P., and M. Reimherr. “Some Recent Developments in Inference for Geostatistical Functional Data”. Revista Colombiana de Estadística, vol. 42, no. 1, Jan. 2019, pp. 101-22, doi:10.15446/rce.v42n1.77058.

Turabian

Kokoszka, Piotr, and Matthew Reimherr. “Some Recent Developments in Inference for Geostatistical Functional Data”. Revista Colombiana de Estadística 42, no. 1 (January 1, 2019): 101–122. Accessed November 13, 2025. https://revistas.unal.edu.co/index.php/estad/article/view/77058.

Vancouver

1.
Kokoszka P, Reimherr M. Some Recent Developments in Inference for Geostatistical Functional Data. Rev. colomb. estad. [Internet]. 2019 Jan. 1 [cited 2025 Nov. 13];42(1):101-22. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/77058

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CrossRef citations12

1. Jeimy-Paola Aristizabal, Ramón Giraldo, Jorge Mateu. (2019). Analysis of variance for spatially correlated functional data: Application to brain data. Spatial Statistics, 32, p.100381. https://doi.org/10.1016/j.spasta.2019.100381.

2. Heng-Hui Lue, ShengLi Tzeng. (2023). Interpretable, predictive spatio-temporal models via enhanced pairwise directions estimation. Journal of Applied Statistics, 50(14), p.2914. https://doi.org/10.1080/02664763.2022.2147150.

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5. Heesang Lee, Dagun Oh, Sunhwa Choi, Jaewoo Park. (2025). Bayesian Function-on-Function Regression for Spatial Functional Data. Bayesian Analysis, -1(-1) https://doi.org/10.1214/25-BA1532.

6. Zhou Zhou, Holger Dette. (2023). Statistical inference for high-dimensional panel functional time series. Journal of the Royal Statistical Society Series B: Statistical Methodology, 85(2), p.523. https://doi.org/10.1093/jrsssb/qkad015.

7. Gregory Bopp, John Ensley, Piotr Kokoszka, Matthew Reimherr. (2022). Geostatistical Functional Data Analysis. Wiley Series in Probability and Statistics. , p.351. https://doi.org/10.1002/9781119387916.ch14.

8. Drew Yarger, Stilian Stoev, Tailen Hsing. (2022). A functional-data approach to the Argo data. The Annals of Applied Statistics, 16(1) https://doi.org/10.1214/21-AOAS1477.

9. Oluwasegun Taiwo Ojo, Marc G. Genton. (2025). Functional multiple-point simulation. Computers & Geosciences, 195, p.105767. https://doi.org/10.1016/j.cageo.2024.105767.

10. Veronika Římalová, Eva Fišerová, Alessandra Menafoglio, Alessia Pini. (2022). Inference for spatial regression models with functional response using a permutational approach. Journal of Multivariate Analysis, 189, p.104893. https://doi.org/10.1016/j.jmva.2021.104893.

11. Hidetoshi Matsui, Kohei Yamamoto, Yuya Yamakawa. (2025). Sparse estimation in kriging for functional data. Stochastic Environmental Research and Risk Assessment, 39(6), p.2413. https://doi.org/10.1007/s00477-025-02976-4.

12. Sergio Martínez, Ramón Giraldo, Víctor Leiva. (2019). Birnbaum–Saunders functional regression models for spatial data. Stochastic Environmental Research and Risk Assessment, 33(10), p.1765. https://doi.org/10.1007/s00477-019-01708-9.

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