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Spatial autoregressive and moving average Hilbertian processes

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  • Ruiz-Medina, M.D.

Abstract

This paper addresses the introduction and study of structural properties of Hilbert-valued spatial autoregressive processes (SARH(1) processes), and Hilbert-valued spatial moving average processes (SMAH(1) processes), with innovations given by two-parameter (spatial) matingale differences. For inference purposes, the conditions under which the tensorial product of standard autoregressive Hilbertian (ARH(1)) processes (respectively, of standard moving average Hilbertian (MAH(1)) processes) is a standard SARH(1) process (respectively, it is a standard SMAH(1) process) are studied. Examples related to the spatial functional observation of two-parameter Markov and diffusion processes are provided. Some open research lines are described in relation to the formulation of SARMAH processes, as well as General Spatial Linear Processes in Functional Spaces.

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  • Ruiz-Medina, M.D., 2011. "Spatial autoregressive and moving average Hilbertian processes," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 292-305, February.
    • Handle: RePEc:eee:jmvana:v:102:y:2011:i:2:p:292-305
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    References listed on IDEAS

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    1. Nerini, David & Monestiez, Pascal & Manté, Claude, 2010. "Cokriging for spatial functional data," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 409-418, February.
    2. Bosq, Denis, 2010. "Tensorial products of functional ARMA processes," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1352-1363, July.
    3. Ruiz-Medina, M.D. & Salmeron, R. & Angulo, J.M., 2007. "Kalman filtering from POP-based diagonalization of ARH(1)," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4994-5008, June.
    4. Yao, Qiwei & Brockwell, Peter J, 2006. "Gaussian maximum likelihood estimation for ARMA models II: spatial processes," LSE Research Online Documents on Economics 5416, London School of Economics and Political Science, LSE Library.
    5. Serge Guillas & Ming-Jun Lai, 2010. "Bivariate splines for spatial functional regression models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(4), pages 477-497.
    6. Veerabhadran Baladandayuthapani & Bani K. Mallick & Mee Young Hong & Joanne R. Lupton & Nancy D. Turner & Raymond J. Carroll, 2008. "Bayesian Hierarchical Spatially Correlated Functional Data Analysis with Application to Colon Carcinogenesis," Biometrics, The International Biometric Society, vol. 64(1), pages 64-73, March.
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    Cited by:

    1. Álvarez-Liébana, J. & Bosq, D. & Ruiz-Medina, M.D., 2017. "Asymptotic properties of a component-wise ARH(1) plug-in predictor," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 12-34.
    2. M. D. Ruiz-Medina & V. V. Anh & R. M. Espejo & J. M. Angulo & M. P. Frías, 2015. "Least-Squares Estimation of Multifractional Random Fields in a Hilbert-Valued Context," Journal of Optimization Theory and Applications, Springer, vol. 167(3), pages 888-911, December.
    3. María P. Frías & Antoni Torres-Signes & María D. Ruiz-Medina & Jorge Mateu, 2022. "Spatial Cox processes in an infinite-dimensional framework," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 175-203, March.
    4. M. D. Ruiz-Medina & D. Miranda & R. M. Espejo, 2019. "Dynamical multiple regression in function spaces, under kernel regressors, with ARH(1) errors," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 943-968, September.
    5. M. D. Ruiz-Medina & R. M. Espejo, 2015. "Maximum-Likelihood Asymptotic Inference for Autoregressive Hilbertian Processes," Methodology and Computing in Applied Probability, Springer, vol. 17(1), pages 207-222, March.
    6. Maria Ruiz-Medina & Rosa Espejo & Elvira Romano, 2014. "Spatial functional normal mixed effect approach for curve classification," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(3), pages 257-285, September.

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