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Some asymptotic results of a non‐parametric conditional mode estimator for functional time‐series data

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  • M'hamed Ezzahrioui
  • Elias Ould Saïd

Abstract

We consider the estimation of the conditional mode function when the covariates take values in some abstract function space. The main goal of this paper was to establish the almost complete convergence and the asymptotic normality of the kernel estimator of the conditional mode when the process is assumed to be strongly mixing and under the concentration property over the functional regressors. Some applications are given. This approach can be applied in time‐series analysis to the prediction and confidence band building. We illustrate our methodology by using El Nio data.

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  • M'hamed Ezzahrioui & Elias Ould Saïd, 2010. "Some asymptotic results of a non‐parametric conditional mode estimator for functional time‐series data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(2), pages 171-201, May.
    • Handle: RePEc:bla:stanee:v:64:y:2010:i:2:p:171-201
    DOI: 10.1111/j.1467-9574.2010.00449.x
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    References listed on IDEAS

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    1. Masry, Elias, 2005. "Nonparametric regression estimation for dependent functional data: asymptotic normality," Stochastic Processes and their Applications, Elsevier, vol. 115(1), pages 155-177, January.
    2. M'hamed Ezzahrioui & Elias Ould-Saïd, 2008. "Asymptotic normality of a nonparametric estimator of the conditional mode function for functional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(1), pages 3-18.
    3. Frédéric Ferraty & Ali Laksaci & Philippe Vieu, 2006. "Estimating Some Characteristics of the Conditional Distribution in Nonparametric Functional Models," Statistical Inference for Stochastic Processes, Springer, vol. 9(1), pages 47-76, May.
    4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    5. Frédéric Ferraty & Philippe Vieu, 2002. "The Functional Nonparametric Model and Application to Spectrometric Data," Computational Statistics, Springer, vol. 17(4), pages 545-564, December.
    6. Ferraty, F. & Vieu, P., 2003. "Curves discrimination: a nonparametric functional approach," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 161-173, October.
    7. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    Cited by:

    1. Mohamed Chaouch & Naâmane Laïb & Djamal Louani, 2017. "Rate of uniform consistency for a class of mode regression on functional stationary ergodic data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(1), pages 19-47, March.
    2. Said Attaoui, 2014. "Strong uniform consistency rates and asymptotic normality of conditional density estimator in the single functional index modeling for time series data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(3), pages 257-286, July.
    3. Kemp, Gordon C.R. & Santos Silva, J.M.C., 2012. "Regression towards the mode," Journal of Econometrics, Elsevier, vol. 170(1), pages 92-101.
    4. Ling, Nengxiang & Wang, Chao & Ling, Jin, 2016. "Modified kernel regression estimation with functional time series data," Statistics & Probability Letters, Elsevier, vol. 114(C), pages 78-85.
    5. Attaoui, Said & Laksaci, Ali & Ould Said, Elias, 2011. "A note on the conditional density estimate in the single functional index model," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 45-53, January.
    6. Ling, Nengxiang & Xu, Qian, 2012. "Asymptotic normality of conditional density estimation in the single index model for functional time series data," Statistics & Probability Letters, Elsevier, vol. 82(12), pages 2235-2243.
    7. Oussama Bouanani & Saâdia Rahmani & Ali Laksaci & Mustapha Rachdi, 2020. "Asymptotic normality of conditional mode estimation for functional dependent data," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(2), pages 465-481, June.
    8. Hamri Mohamed Mehdi & Dib Abdassamad & Rabhi Abbes, 2022. "Asymptotic Properties of the Estimator of the Conditional Distribution for Associated Functional Data," Econometrics. Advances in Applied Data Analysis, Sciendo, vol. 26(3), pages 21-34, September.

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