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Consistency of a nonparametric conditional mode estimator for random fields

Author

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  • Sophie Dabo-Niang
  • Sidi Ould-Abdi
  • Ahmedoune Ould-Abdi
  • Aliou Diop

Abstract

Given a stationary multidimensional spatial process $$\left\{ Z_{\mathbf{i}}=\left( X_{\mathbf{i}},\ Y_{\mathbf{i}}\right) \in \mathbb R ^d\right. \left. \times \mathbb R ,\mathbf{i}\in \mathbb Z ^{N}\right\} $$ Z i = X i , Y i ∈ R d × R , i ∈ Z N , we investigate a kernel estimate of the spatial conditional mode function of the response variable $$Y_{\mathbf{i}}$$ Y i given the explicative variable $$X_{\mathbf{i}}$$ X i . Consistency in $$L^p$$ L p norm and strong convergence of the kernel estimate are obtained when the sample considered is a $$\alpha $$ α -mixing sequence. An application to real data is given in order to illustrate the behavior of our methodology. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Sophie Dabo-Niang & Sidi Ould-Abdi & Ahmedoune Ould-Abdi & Aliou Diop, 2014. "Consistency of a nonparametric conditional mode estimator for random fields," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(1), pages 1-39, March.
    • Handle: RePEc:spr:stmapp:v:23:y:2014:i:1:p:1-39
    DOI: 10.1007/s10260-013-0239-2
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    References listed on IDEAS

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    Cited by:

    1. Mohammed Attouch & Ali Laksaci & Nafissa Messabihi, 2017. "Nonparametric relative error regression for spatial random variables," Statistical Papers, Springer, vol. 58(4), pages 987-1008, December.
    2. S.‐H. Arnaud Kanga & Ouagnina Hili & Sophie Dabo‐Niang & Assi N'Guessan, 2023. "Asymptotic properties of nonparametric quantile estimation with spatial dependency," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(3), pages 254-283, August.
    3. Ahmad Aboubacrène Ag & Deme El Hadji & Diop Aliou & Girard Stéphane, 2019. "Estimation of the tail-index in a conditional location-scale family of heavy-tailed distributions," Dependence Modeling, De Gruyter, vol. 7(1), pages 394-417, January.
    4. 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.

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