Abstract
This paper extends to the Banach-valued framework previous strong-consistency results derived, in the context of diagonal componentwise estimation of the autocorrelation operator of autoregressive Hilbertian processes, and the associated plug-in prediction. The Banach space B considered here is \( B = {\fancyscript{C}}\left( {\left[ {0,1} \right]} \right) \), the space of continuous functions on [0, 1] with the supremum norm.
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Álvarez-Liébana, J., Ruiz-Medina, M.D. (2017). A diagonal componentwise approach for ARB(1) prediction. In: Aneiros, G., G. Bongiorno, E., Cao, R., Vieu, P. (eds) Functional Statistics and Related Fields. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-55846-2_4
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DOI: https://doi.org/10.1007/978-3-319-55846-2_4
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