Prediction of functional data with spatial dependence: a penalized approach
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Spatial functional dataSpatial correlationP-spline penaltyFunctional regression
Aguilera-Morillo, M.C., Durbán, M. & Aguilera, A.M. Prediction of functional data with spatial dependence: a penalized approach. Stoch Environ Res Risk Assess 31, 7–22 (2017). https://doi.org/10.1007/s00477-016-1216-8
SponsorshipProject P11-FQM-8068 from Consejería de Innovación, Ciencia y Empresa, Junta de Andalucía, Spain; Projects MTM2013-47929-P, MTM2011-28285-C02-C2 and MTM 2014-52184-P from Secretaría de Estado Investigación, Desarrollo e Innovación, Ministerio de Economía y Competitividad, Spain
This paper is focus on spatial functional variables whose observations are a set of spatially correlated sample curves obtained as realizations of a spatio-temporal stochastic process. In this context, as alternative to other geostatistical techniques (kriging, kernel smoothing, among others), a new method to predict the curves of temporal evolution of the process at unsampled locations and also the surfaces of geographical evolution of the variable at unobserved time points is proposed. In order to test the good performance of the proposed method, two simulation studies and an application with real climatological data have been carried out. Finally, the results were compared with ordinary functional kriging.