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Rates of convergence of autocorrelation estimates for autoregressive Hilbertian processes

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  • Guillas, Serge
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    Abstract

    We show consistency in the mean integrated quadratic sense of an estimator of the autocorrelation operator [rho] in the autoregressive Hilbertian of order one model. Two main cases are considered, and we obtain upper bounds for the corresponding rates.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 55 (2001)
    Issue (Month): 3 (December)
    Pages: 281-291

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    Handle: RePEc:eee:stapro:v:55:y:2001:i:3:p:281-291

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    Keywords: Hilbert space Autoregressive processes Estimation Rate of convergence Functional data;

    References

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    1. Cardot, Hervé & Ferraty, Frédéric & Sarda, Pascal, 1999. "Functional linear model," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 11-22, October.
    2. Philippe C. Besse, 2000. "Autoregressive Forecasting of Some Functional Climatic Variations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 27(4), pages 673-687.
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    Cited by:
    1. Ruiz-Medina, M.D. & Salmeron, R. & Angulo, J.M., 2007. "Kalman filtering from POP-based diagonalization of ARH(1)," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4994-5008, June.

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