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Revista Colombiana de Estadística
Print version ISSN 0120-1751
Rev.Colomb.Estad. vol.42 no.1 Bogotá Jan./June 2019 Epub May 23, 2019
https://doi.org/10.15446/rce.v42n1.77058
Artículos originales de investigación
Some Recent Developments in Inference for Geostatistical Functional Data
Algunos desarrollos recientes en inferencia para datos funcionales geoestadísticos
a Department of Statistics, Colorado State University, Fort Collins, USA. E-mail: Piotr.Kokoszka@colostate.edu
b Department of Statistics, Penn State University, State College, USA. E-mail: mreimherr@psu.edu
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.
Key words: Functional data; Spatial statistics
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 o 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.
Palabras clave: Datos funcionales; Estadística espacial
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. [ Links ]
Beirlant, J., Goegebeur, Y., Segers, J. & Teugels, J. (2006), Statistics of Extremes: Theory and Applications, John Wiley & Sons. [ Links ]
Caballero, W., Giraldo, R. & Mateu, J. (2013), 'A universal kriging approach for spatial functional data', Stochastic Environmental Research and Risk Assessment 27, 1553-1563. [ Links ]
Constantinou, P., Kokoszka, P. & Reimherr, M. (2017), 'Testing separability of space-time functional processes', Biometrika 104, 425-437. [ Links ]
Csörg®, M. & Horváth, L. (1997), Limit Theorems in Change-Point Analysis, Wiley. [ Links ]
Delicado, P., Giraldo, R., Comas, C. & Mateu, J. (2010), 'Statistics for spatial functional data: some recent contributions', Environmetrics 21, 224-239. [ Links ]
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. [ Links ]
Gelfand, A. E., Diggle, P. J., Fuentes, M. & Guttorp, P., eds (2010), Handbook of Spatial Statistics, CRC Press. [ Links ]
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. [ Links ]
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. [ Links ]
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. [ Links ]
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. [ Links ]
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. [ Links ]
Hörmann, S. & Kokoszka, P. (2013), 'Consistency of the mean and the principal components of spatially distributed functional data', Bernoulli 19, 1535-1558. [ Links ]
Horváth, L. & Kokoszka, P. (2012), Inference for Functional Data with Applications, Springer. [ Links ]
Kokoszka, P. & Reimherr, M. (2017), Introduction to Functional Data Analysis, CRC Press. [ Links ]
Liu, C., Ray, S. & Hooker, G. (2017), 'Functional principal components analysis of spatially correlated data', Statistics and Computing 27, 1639-1654. [ Links ]
Lu, N. & Zimmerman, D. (2005), 'The likelihood ratio test for a separable covariance matrix', Statistics & Probability Letters 73, 449-457. [ Links ]
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. [ Links ]
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. [ Links ]
Rishbeth, H. (1990), 'A greenhouse effect in the ionosphere?', Planetary and Space Science 38, 945-948. [ Links ]
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. [ Links ]
Schabenberger, O. & Gotway, C. A. (2005), Statistical Methods for Spatial Data Analysis, Chapman & Hall/CRC. [ Links ]
Sherman, M. (2011), Spatial Statistics and Spatio-Temporal Data: Covariance Functions and Directional Properties, Wiley. [ Links ]
Wackernagel, H. (2003), Multivariate Geostatistics, Springer. [ Links ]
Received: January 2017; Accepted: November 2018