Resolvent estimators for functional autoregressive processes with random coefficients

Souad Boukhiar and Tahar Mourid

Journal of Multivariate Analysis, 2022, vol. 189, issue C

Abstract: We deal with resolvent estimators of the mean of random operators ruling a functional autoregressive process equation. Under mild conditions on the decay rate of a regularizing parameter, we obtain convergence in probability, exponential bounds, almost sure convergence and limiting law of the estimators and as well as results on resolvent predictors. These estimators achieve parametric rate n (up to a logn factor). Then we propose an estimator of the variance of random operators and show its convergence. These results extend and improve those of Mas in the framework of functional AR Processes with deterministic coefficients. Simulated and real data examples are used to illustrate the performance of these predictors and showing competitive results.

Keywords: AR process; Covariance operators; Functional data; Random coefficients; Resolvent estimators (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.jmva.2021.104884

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