Optimal rate for covariance operator estimators of functional autoregressive processes with random coefficients

Abdelaziz Allam and Tahar Mourid

Journal of Multivariate Analysis, 2019, vol. 169, issue C, 130-137

Abstract: We improve a result of Allam and Mourid (2014) by deriving the optimal n rate for the empirical covariance operators of a Hilbert-valued autoregressive process with random coefficients. Our approach is based on a suitable autoregressive representation of a sequence of covariance operators related to the model, which leads to a decomposition with Hilbert-valued martingale differences. Using large deviation inequalities for Hilbert-valued martingale differences, we then establish exponential bounds and derive the almost sure convergence of the empirical covariance operators in the Hilbert–Schmidt norm, achieving the parametric rate n up to a ln(n) factor in the bounded process case.

Date: 2019
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.jmva.2018.07.009

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