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Estimation of the regression operator from functional fixed-design with correlated errors

  • Benhenni, K.
  • Hedli-Griche, S.
  • Rachdi, M.
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    We consider the estimation of the regression operator r in the functional model: Y=r(x)+[epsilon], where the explanatory variable x is of functional fixed-design type, the response Y is a real random variable and the error process [epsilon] is a second order stationary process. We construct the kernel type estimate of r from functional data curves and correlated errors. Then we study their performances in terms of the mean square convergence and the convergence in probability. In particular, we consider the cases of short and long range error processes. When the errors are negatively correlated or come from a short memory process, the asymptotic normality of this estimate is derived. Finally, some simulation studies are conducted for a fractional autoregressive integrated moving average and for an Ornstein-Uhlenbeck error processes.

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    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 101 (2010)
    Issue (Month): 2 (February)
    Pages: 476-490

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    Handle: RePEc:eee:jmvana:v:101:y:2010:i:2:p:476-490
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    1. K. Benhenni & F. Ferraty & M. Rachdi & P. Vieu, 2007. "Local smoothing regression with functional data," Computational Statistics, Springer, vol. 22(3), pages 353-369, September.
    2. Benhenni, K. & Hedli-Griche, S. & Rachdi, M. & Vieu, P., 2008. "Consistency of the regression estimator with functional data under long memory conditions," Statistics & Probability Letters, Elsevier, vol. 78(8), pages 1043-1049, June.
    3. Boente, Graciela & Fraiman, Ricardo, 2000. "Kernel-based functional principal components," Statistics & Probability Letters, Elsevier, vol. 48(4), pages 335-345, July.
    4. Roussas, G. G., 1994. "Asymptotic Normality of Random Fields of Positively or Negatively Associated Processes," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 152-173, July.
    5. Roussas, George G., 2000. "Asymptotic normality of the kernel estimate of a probability density function under association," Statistics & Probability Letters, Elsevier, vol. 50(1), pages 1-12, October.
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