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Nonparametric prediction of spatial multivariate data

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  • Sophie Dabo-Niang
  • Camille Ternynck
  • Anne-Françoise Yao

Abstract

This paper investigates a nonparametric spatial predictor of a stationary multidimensional spatial process observed over a rectangular domain. The proposed predictor depends on two kernels in order to control both the distance between observations and that between spatial locations. The uniform almost complete consistency and the asymptotic normality of the kernel predictor are obtained when the sample considered is an alpha-mixing sequence. Numerical studies were carried out in order to illustrate the behaviour of our methodology both for simulated data and for an environmental data set.

Suggested Citation

  • Sophie Dabo-Niang & Camille Ternynck & Anne-Françoise Yao, 2016. "Nonparametric prediction of spatial multivariate data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(2), pages 428-458, June.
    • Handle: RePEc:taf:gnstxx:v:28:y:2016:i:2:p:428-458
    DOI: 10.1080/10485252.2016.1164313
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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.
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    3. Mohamed Machkouri, 2007. "Nonparametric Regression Estimation for Random Fields in a Fixed-Design," Statistical Inference for Stochastic Processes, Springer, vol. 10(1), pages 29-47, January.
    4. Gérard Biau & Benoît Cadre, 2004. "Nonparametric Spatial Prediction," Statistical Inference for Stochastic Processes, Springer, vol. 7(3), pages 327-349, October.
    5. Mohamed El Machkouri & Radu Stoica, 2010. "Asymptotic normality of kernel estimates in a regression model for random fields," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(8), pages 955-971.
    6. 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.
    7. Tran, Lanh Tat, 1990. "Kernel density estimation on random fields," Journal of Multivariate Analysis, Elsevier, vol. 34(1), pages 37-53, July.
    8. Mohamed El Machkouri, 2011. "Asymptotic normality of the Parzen–Rosenblatt density estimator for strongly mixing random fields," Statistical Inference for Stochastic Processes, Springer, vol. 14(1), pages 73-84, February.
    9. Hongxia Wang & Jinde Wang & Bo Huang, 2012. "Prediction for spatio-temporal models with autoregression in errors," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(1), pages 217-244.
    10. Bel, L. & Allard, D. & Laurent, J.M. & Cheddadi, R. & Bar-Hen, A., 2009. "CART algorithm for spatial data: Application to environmental and ecological data," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 3082-3093, June.
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    Cited by:

    1. Rodrigo García Arancibia & Pamela Llop & Mariel Lovatto, 2023. "Nonparametric prediction for univariate spatial data: Methods and applications," Papers in Regional Science, Wiley Blackwell, vol. 102(3), pages 635-672, June.
    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. Bouzebda, Salim & Slaoui, Yousri, 2019. "Large and moderate deviation principles for recursive kernel estimators of a regression function for spatial data defined by stochastic approximation method," Statistics & Probability Letters, Elsevier, vol. 151(C), pages 17-28.

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