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Asymptotic normality of kernel estimates in a regression model for random fields

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  • Mohamed El Machkouri
  • Radu Stoica

Abstract

We establish the asymptotic normality of the regression estimator in a fixed-design setting when the errors are given by a field of dependent random variables. The result applies to martingale-difference or strongly mixing random fields. On this basis, a statistical test that can be applied to image analysis is also presented.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:gnstxx:v:22:y:2010:i:8:p:955-971
    DOI: 10.1080/10485250903505893
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    Citations

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    Cited by:

    1. Younso, Ahmad, 2017. "On the consistency of a new kernel rule for spatially dependent data," Statistics & Probability Letters, Elsevier, vol. 131(C), pages 64-71.
    2. Bouabsa Wahiba, 2022. "Unform in Bandwith of the Conditional Distribution Function with Functional Explanatory Variable: The Case of Spatial Data with the K Nearest Neighbour Method," Econometrics. Advances in Applied Data Analysis, Sciendo, vol. 26(2), pages 30-46, June.
    3. 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.
    4. 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.
    5. 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.
    6. Peligrad, Magda & Sang, Hailin & Xiao, Yimin & Yang, Guangyu, 2022. "Limit theorems for linear random fields with innovations in the domain of attraction of a stable law," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 596-621.

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