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Covariance operator estimation of a functional autoregressive process with random coefficients

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  • Allam, Abdelaziz
  • Mourid, Tahar

Abstract

We deal with the covariance and cross covariance operators estimation of a Hilbert space valued autoregressive process with random coefficients. We establish bounds for empirical estimators in mean square error and almost sure convergence in Hilbert–Schmidt norm. Consistent estimators of the eigenvalues are also derived.

Suggested Citation

  • Allam, Abdelaziz & Mourid, Tahar, 2014. "Covariance operator estimation of a functional autoregressive process with random coefficients," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 1-8.
    • Handle: RePEc:eee:stapro:v:84:y:2014:i:c:p:1-8
    DOI: 10.1016/j.spl.2013.09.018
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    References listed on IDEAS

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    Cited by:

    1. Allam, Abdelaziz & Mourid, Tahar, 2019. "Optimal rate for covariance operator estimators of functional autoregressive processes with random coefficients," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 130-137.

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