Proyectos
GEOSTATISTICAL ANALYSIS OF FUNCTIONAL DATA: TWO NEW APPROACHES
Resumen
In the same way that standard statistical methods have been generalized to be used in FDA, it is possible to think that geostatistical methods can be adapted to these types of data. This topic has been considered from several points of view. Goulard & Voltz (1993) is a pioneer work in the spatial prediction of curves setting. They propose three geostatistical approaches to predict curves: a curve kriging approach and two multivariate approaches based on cokriging on either discrete data or coefficients of the parametric models that have been fitted to the observed curves. Giraldo et al (2008) solve the problem of spatial prediction of functional data by weighting each observed curve by a functional parameter. This approach is a combination of ordinary kriging and the functional linear concurrent model such as shown in Chapter 14 of Ramsay & Silverman (2005). This approach was mentioned in Goulard & Voltz (1993) but was not developed there. Giraldo et al (2009) propose a cokriging predictor for doing univariate prediction (as in the cokriging multivariable sense), but considering as auxiliary information samples of curves instead of observations of random vectors. Likewise, they extend the multivariable kriging from random vectors to the functional context by defining a functional kriging predictor which allows to do prediction of a whole curve at an unvisited site by using as information the curves sampled in nearby sites to the prediction site. This problem is also studied by Nerini & Monestiez (2008). They propose a solution based on orthonormal basis functions. There is still a long way of research necessary for spatial prediction of functional data. In this project we consider the problem of carrying out spatial prediction based on spatially referenced information of scalars and functional variables.
Convocatoria
Nombre de la convocatoria:Proyectos Jornada Docente
Modalidad:Proyectos Jornada Docente
Responsable