Strongly consistent autoregressive predictors in abstract Banach spaces

Autor:	Ruiz-Medina, MD, Alvarez-Liebana, J.
Rok vydání:	2018
Předmět:	Mathematics - Statistics Theory
Druh dokumentu:	Working Paper
Popis:	This work derives new results on strong consistent estimation and prediction for autoregressive processes of order 1 in a separable Banach space B. The consistency results are obtained for the component-wise estimator of the autocorrelation operator in the norm of the space L(B) of bounded linear operators on B. The strong consistency of the associated plug-in predictor then follows in the B-norm. A Gelfand triple is defined through the Hilbert space constructed in Kuelbs (1970)' lemma. A Hilbert--Schmidt embedding introduces the Reproducing Kernel Hilbert space (RKHS), generated by the autocovariance operator, into the Hilbert space conforming the Rigged Hilbert space structure. This paper extends the work of Bosq (2000) and Labbas and Mourid 2002. Comment: This paper has been accepted in Journal of Multivariate Analysis, it will appear in 2019. arXiv admin note: substantial text overlap with arXiv:1801.08817
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1808.01659 Zobrazit plný text záznamu View this record from Arxiv