2026-06-28T10:05:09Zhttps://docta.ucm.es/rest/oai/request
oai:docta.ucm.es:20.500.14352/953362025-03-31T23:50:13Zcom_20.500.14352_14col_20.500.14352_15
Docta Complutense author Álvarez Liébana, Javier author Bosq, Denis author Ruiz Medina, María Dolores 2024-01-25T10:32:40Z 2024-01-25T10:32:40Z 2017 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. 0047-259X 10.1016/j.jmva.2016.11.009 https://hdl.handle.net/20.500.14352/95336 https://doi.org/10.1016/j.jmva.2016.11.009 https://www-sciencedirect-com.bucm.idm.oclc.org/journal/journal-of-multivariate-analysishttps://www.sciencedirect.com/science/article/pii/S0047259X16301737 This paper presents new results on the prediction of linear processes in function spaces. The autoregressive Hilbertian process framework of order one (ARH(1) framework) is adopted. A component-wise estimator of the autocorrelation operator is derived from the momentbased estimation of its diagonal coefficients with respect to the orthogonal eigenvectors of the autocovariance operator, which are assumed to be known. Mean-square convergence to the theoretical autocorrelation operator is proved in the space of Hilbert–Schmidt operators. Consistency then follows in that space. Mean absolute convergence, in the underlying Hilbert space, of the ARH(1) plug-in predictor to the conditional expectation is obtained as well. A simulation study is undertaken to illustrate the large-sample behavior of the formulated component-wise estimator and predictor. Additionally, alternative component-wise (with known and unknown eigenvectors), regularized, wavelet-based penalized, and nonparametric kernel estimators of the autocorrelation operator are compared with the one presented here, in terms of prediction eng Attribution-NonCommercial-NoDerivatives 4.0 International Asymptotic properties of a component-wise ARH(1) plug-in predictor journal article 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URL https://docta.ucm.es/bitstreams/21a90ebd-8dfe-410d-8a03-d7f93718eea2/download File MD5 be0bcc7168c131468e5ae3d9b1d2a521 628866 application/pdf Asymptotic_properties.pdf