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A note on strong-consistency of componentwise ARH(1) predictors

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  • Ruiz-Medina, M.D.
  • Álvarez-Liébana, J.

Abstract

New results on strong-consistency in the trace operator norm are obtained, in the parameter estimation of an autoregressive Hilbertian process of order one (ARH(1) process). Additionally, a strongly-consistent diagonal componentwise estimator of the autocorrelation operator is derived, based on its empirical singular value decomposition.

Suggested Citation

  • Ruiz-Medina, M.D. & Álvarez-Liébana, J., 2019. "A note on strong-consistency of componentwise ARH(1) predictors," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 224-228.
    • Handle: RePEc:eee:stapro:v:145:y:2019:i:c:p:224-228
    DOI: 10.1016/j.spl.2018.09.004
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    References listed on IDEAS

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    1. Álvarez-Liébana, Javier & Bosq, Denis & Ruiz-Medina, María D., 2016. "Consistency of the plug-in functional predictor of the Ornstein–Uhlenbeck process in Hilbert and Banach spaces," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 12-22.
    2. Frédéric Ferraty & Aldo Goia & Philippe Vieu, 2002. "Functional nonparametric model for time series: a fractal approach for dimension reduction," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(2), pages 317-344, December.
    3. Mas, André, 2007. "Weak convergence in the functional autoregressive model," Journal of Multivariate Analysis, Elsevier, vol. 98(6), pages 1231-1261, July.
    4. André Mas, 1999. "Normalité asymptotique de l’estimateur empirique de l’opérateur d’autocorrélation d’un processus ARH(1)," Working Papers 99-11, Center for Research in Economics and Statistics.
    5. Aldo Goia & Philippe Vieu, 2015. "A partitioned Single Functional Index Model," Computational Statistics, Springer, vol. 30(3), pages 673-692, September.
    6. Aneiros-Pérez, Germán & Vieu, Philippe, 2006. "Semi-functional partial linear regression," Statistics & Probability Letters, Elsevier, vol. 76(11), pages 1102-1110, June.
    7. Petrovich, Justin & Reimherr, Matthew, 2017. "Asymptotic properties of principal component projections with repeated eigenvalues," Statistics & Probability Letters, Elsevier, vol. 130(C), pages 42-48.
    8. Álvarez-Liébana, J. & Bosq, D. & Ruiz-Medina, M.D., 2017. "Asymptotic properties of a component-wise ARH(1) plug-in predictor," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 12-34.
    9. Ferraty, F. & Van Keilegom, I. & Vieu, P., 2012. "Regression when both response and predictor are functions," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 10-28.
    10. Aneiros-Pérez, Germán & Vieu, Philippe, 2008. "Nonparametric time series prediction: A semi-functional partial linear modeling," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 834-857, May.
    11. Guillas, Serge, 2001. "Rates of convergence of autocorrelation estimates for autoregressive Hilbertian processes," Statistics & Probability Letters, Elsevier, vol. 55(3), pages 281-291, December.
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