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Asymptotic properties of the kernel estimate of spatial conditional mode when the regressor is functional

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  • Sophie Dabo-Niang
  • Zoulikha Kaid
  • Ali Laksaci

Abstract

The kernel method estimator of the spatial modal regression for functional regressors is proposed. We establish, under some general mixing conditions, the $$L^p$$ L p -consistency and the asymptotic normality of the estimator. The performance of the proposed estimator is illustrated in a real data application. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:alstar:v:99:y:2015:i:2:p:131-160
    DOI: 10.1007/s10182-014-0233-5
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    References listed on IDEAS

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    1. Gérard Biau & Benoît Cadre, 2004. "Nonparametric Spatial Prediction," Statistical Inference for Stochastic Processes, Springer, vol. 7(3), pages 327-349, October.
    2. Carbon, Michel & Tran, Lanh Tat & Wu, Berlin, 1997. "Kernel density estimation for random fields (density estimation for random fields)," Statistics & Probability Letters, Elsevier, vol. 36(2), pages 115-125, December.
    3. Tran, Lanh Tat, 1990. "Kernel density estimation on random fields," Journal of Multivariate Analysis, Elsevier, vol. 34(1), pages 37-53, July.
    4. 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.
    5. Dabo-Niang, Sophie & Thiam, Baba, 2010. "Robust quantile estimation and prediction for spatial processes," Statistics & Probability Letters, Elsevier, vol. 80(17-18), pages 1447-1458, September.
    6. Lu, Zudi & Chen, Xing, 2004. "Spatial kernel regression estimation: weak consistency," Statistics & Probability Letters, Elsevier, vol. 68(2), pages 125-136, June.
    7. Gao, Jiti & Lu, Zudi & Tjøstheim, Dag, 2008. "Moment inequalities for spatial processes," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 687-697, April.
    8. Sophie Dabo-Niang & Ali Laksaci, 2010. "Note on conditional mode estimation for functional dependent data," Statistica, Department of Statistics, University of Bologna, vol. 70(1), pages 83-94.
    9. Marc Hallin & Michel Carbon & Lanh T. Tran, 1996. "Kernel density estimation on random fields: the L1 theory," ULB Institutional Repository 2013/2065, ULB -- Universite Libre de Bruxelles.
    10. 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.
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    Cited by:

    1. Somia Ayad & Ali Laksaci & Saâdia Rahmani & Rachida Rouane, 2020. "On the local linear modelization of the conditional density for functional and ergodic data," METRON, Springer;Sapienza Università di Roma, vol. 78(2), pages 237-254, August.
    2. Fahimah A. Al-Awadhi & Zoulikha Kaid & Ali Laksaci & Idir Ouassou & Mustapha Rachdi, 2019. "Functional data analysis: local linear estimation of the $$L_1$$ L 1 -conditional quantiles," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(2), pages 217-240, June.
    3. 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).

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