This article is published in Environmetrics as a special issue on Spatio-Temporal Stochastic Modelling (METMAV), edited by Wenceslao González-Manteiga and Rosa M. Crujeiras, University of Santiago de Compostela, Spain.
Special Issue Paper
Spatial functional prediction from spatial autoregressive Hilbertian processes†
Version of Record online: 23 NOV 2011
Copyright © 2011 John Wiley & Sons, Ltd.
Special Issue: Spatio-Temporal Stochastic Modelling. (METMAV)
Volume 23, Issue 1, pages 119–128, February 2012
How to Cite
Ruiz-Medina, M. D. (2012), Spatial functional prediction from spatial autoregressive Hilbertian processes. Environmetrics, 23: 119–128. doi: 10.1002/env.1143
- Issue online: 16 JAN 2012
- Version of Record online: 23 NOV 2011
- Manuscript Accepted: 29 OCT 2011
- Manuscript Revised: 27 OCT 2011
- Manuscript Received: 7 JAN 2011
- DGI, MEC. Grant Number: MTM2009-13393
- Andalousian CICE, Spain. Grant Number: P09-FQM-5052
- diagonalization of infinite-dimensional parameters;
- projection estimators;
- spatial autoregressive functional series;
- spatial functional prediction;
- two-parameter diffusion processes
The class of spatial autoregressive Hilbertian models (SARH(1) processes) is considered. The projection estimation methodology proposed here is based on the biorthogonal eigenfunction bases diagonalizing the infinite-dimensional parameters involved in the SARH(1) state equation. These bases remove the ill-posed nature of the functional equation system defining the moment-based estimators of such parameters. The performance of the proposed projection estimation methodology, in the SARH(1) context, is illustrated in terms of simulated and real-data examples. In particular, this methodology provides a suitable spatial functional extrapolation of tropical and subtropical weak-dependence ocean surface temperature profiles, in the absence of high spatial concentration of weather stations, removing computational problems associated with matrix determinant close to zero. Copyright © 2011 John Wiley & Sons, Ltd.