Some Recent Developments in Inference for Geostatistical Functional Data

• Autores: Piotr Kokoszka, Matthew Reimherr
• Localización: Revista Colombiana de Estadística, ISSN-e 2389-8976, ISSN 0120-1751, Vol. 42, Nº. 1, 2019, págs. 101-122
• Idioma: inglés
• DOI: 10.15446/rce.v42n1.77058
• Títulos paralelos:
  • Algunos desarrollos recientes en inferencia para datos funcionales geoestadísticos
• Enlaces
  • Texto completo
• Resumen
  • español

    Resumen 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.

  • English

    Abstract 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.

• Referencias bibliográficas
  • Aston, J.,Pigoli, D.,Tavakoli, S. (2016). Tests for separability in nonparametric covariance operators of random surfaces. The Annals of Statistics....
  • 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...
  • Constantinou, P.,Kokoszka, P.,Reimherr, M. (2017). Testing separability of space-time functional processes. Biometrika. 104. 425
  • Csörg®, 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....
  • French, J.,Kokoszka, P.,Stoev, S.,Hall, L. (2019). Quantifying the risk of heat waves using extreme value theory and spatio-temporal functional...
  • Gelfand, A. E.,Diggle, P. J.,Fuentes, M.,Guttorp, P. (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...
  • Gromenko, O.,Kokoszka, P. (2013). Nonparametric inference in small data sets of spatially indexed curves with application to ionospheric trend...
  • Gromenko, O.,Kokoszka, P.,Reimherr, M. (2017). Detection of change in the spatiotemporal mean function. Journal of the Royal Statistical Society....
  • Gromenko, O.,Kokoszka, P.,Sojka, J. (2017). Evaluation of the global cooling trend in the ionosphere using functional regression models with...
  • Gromenko, O.,Kokoszka, P.,Zhu, L.,Sojka, J. (2012). Estimation and testing for spatially indexed curves with application to ionospheric and...
  • Hörmann, S.,Kokoszka, P. (2013). Consistency of the mean and the principal components of spatially distributed functional data. Bernoulli....
  • 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
  • Lu, N.,Zimmerman, D. (2005). The likelihood ratio test for a separable covariance matrix. Statistics & Probability Letters. 73. 449
  • Menafoglio, A.,Secchi, P.,Rosa, M. D. (2013). A universal kriging predictor for spatially dependent functional data of a hilbert space. Electronic...
  • Mitchell, M. W.,Genton, M. G.,Gumpertz, M. L. (2006). A likelihood ratio test for separability of covariances. Journal of Multivariate Analysis....
  • Rishbeth, H. (1990). A greenhouse effect in the ionosphere?. Planetary and Space Science. 38. 945
  • Roble, R. G.,Dickinson, R. E. (1989). How will changes in carbon dioxide and methane modify the mean structure of the mesosphere and thermosphere?....
  • 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.