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Asymptotic normality of a nonparametric estimator of the conditional mode function for functional data

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  • M'hamed Ezzahrioui
  • Elias Ould-Saïd

Abstract

We consider the estimation of the conditional mode function when the covariables take values in some abstract function space. It is shown that, under some regularity conditions, the kernel estimate of the conditional mode is asymptotically normally distributed. From this, we derive the asymptotic normality of a predictor and propose confidence bands for the conditional mode function. Simulations are drawn to show how our methodology can be implemented.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:gnstxx:v:20:y:2008:i:1:p:3-18
    DOI: 10.1080/10485250701541454
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    Cited by:

    1. Salim Bouzebda & Christophe Chesneau, 2020. "A Note on the Nonparametric Estimation of the Conditional Mode by Wavelet Methods," Stats, MDPI, vol. 3(4), pages 1-9, October.
    2. Rachdi, Mustapha & Laksaci, Ali & Demongeot, Jacques & Abdali, Abdel & Madani, Fethi, 2014. "Theoretical and practical aspects of the quadratic error in the local linear estimation of the conditional density for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 53-68.
    3. Akkal Fatima & Kadiri Nadia & Rabhi Abbes, 2021. "Asymptotic Normality of Conditional Density and Conditional Mode in the Functional Single Index Model," Econometrics. Advances in Applied Data Analysis, Sciendo, vol. 25(1), pages 1-24, March.
    4. Liu, Qiaojing & Zhao, Shoujiang, 2013. "Pointwise and uniform moderate deviations for nonparametric regression function estimator on functional data," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1372-1381.
    5. Amel, Azzi & Ali, Laksaci & Elias, Ould Saïd, 2022. "On the robustification of the kernel estimator of the functional modal regression," Statistics & Probability Letters, Elsevier, vol. 181(C).
    6. Sophie Dabo-Niang & Zoulikha Kaid & Ali Laksaci, 2015. "Asymptotic properties of the kernel estimate of spatial conditional mode when the regressor is functional," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(2), pages 131-160, April.
    7. Azzedine, Nadjia & Laksaci, Ali & Ould-Saïd, Elias, 2008. "On robust nonparametric regression estimation for a functional regressor," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3216-3221, December.
    8. Frédéric Ferraty & Nadia Kudraszow & Philippe Vieu, 2012. "Nonparametric estimation of a surrogate density function in infinite-dimensional spaces," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(2), pages 447-464.
    9. Kudraszow, Nadia L. & Vieu, Philippe, 2013. "Uniform consistency of kNN regressors for functional variables," Statistics & Probability Letters, Elsevier, vol. 83(8), pages 1863-1870.
    10. 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.
    11. Dabo-Niang, Sophie & Kaid, Zoulikha & Laksaci, Ali, 2012. "On spatial conditional mode estimation for a functional regressor," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1413-1421.
    12. 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.
    13. Laib, Naâmane & Louani, Djamal, 2010. "Nonparametric kernel regression estimation for functional stationary ergodic data: Asymptotic properties," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2266-2281, November.

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