RT Journal Article
T1 Asymptotic properties of a component-wise ARH(1) plug-in predictor
A1 Álvarez Liébana, Javier
A1 Bosq, Denis
A1 Ruiz Medina, María Dolores
AB 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
PB Elsevier
SN 0047-259X
YR 2017
FD 2017
LK https://hdl.handle.net/20.500.14352/95336
UL https://hdl.handle.net/20.500.14352/95336
LA eng
NO 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.
NO Supplementary Material: Asymptotic properties of a componentwise ARH(1) plug-in predictor: https://ars.els-cdn.com/content/image/1-s2.0-S0047259X16301737-mmc1.pdf
NO Ministerio de Economía, Comercio y Empresa (España)
DS Docta Complutense
RD 26 abr 2025