Almost Sure convergence of the Resolvent Estimators for Hilbertian Autoregressive Processes - Les annales de l'ISUP
Journal Articles Annales de l'ISUP Year : 2019

Almost Sure convergence of the Resolvent Estimators for Hilbertian Autoregressive Processes

Abstract

We consider the class of resolvent estimators of the corrélation operator ruling the functional autoregressive processes introduced by Mas, A. ([10] [11]). Under mild conditions on smoothing parameter, we establish exponential bounds and almost sure convergence of the resolvent estimators as well as convergence rates improving the existing results. As a conséquence we dérivé asymptotic results on the resolvent predictors. Numerical studies illustrate the performance of the resolvent predictors giving a comparison with other existing prédiction methods both on simulated and real functional data sets showing compétitive results.
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Dates and versions

hal-03604215 , version 1 (10-03-2022)

Identifiers

  • HAL Id : hal-03604215 , version 1

Cite

Souad Boukhiar, Tahar Mourid. Almost Sure convergence of the Resolvent Estimators for Hilbertian Autoregressive Processes. Annales de l'ISUP, 2019, 63 (2-3), pp.129-142. ⟨hal-03604215⟩

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