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On local linear regression for strongly mixing random fields

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  • El Machkouri, Mohamed
  • Es-Sebaiy, Khalifa
  • Ouassou, Idir

Abstract

We investigate the local linear kernel estimator of the regression function g of a stationary and strongly mixing real random field observed over a general subset of the lattice Zd. Assuming that g is differentiable with derivative g′, we provide a new criterion on the mixing coefficients for the consistency and the asymptotic normality of the estimators of g and g′ under mild conditions on the bandwidth parameter. Our results improve the work of Hallin et al. (2004) in several directions.

Suggested Citation

  • El Machkouri, Mohamed & Es-Sebaiy, Khalifa & Ouassou, Idir, 2017. "On local linear regression for strongly mixing random fields," Journal of Multivariate Analysis, Elsevier, vol. 156(C), pages 103-115.
    • Handle: RePEc:eee:jmvana:v:156:y:2017:i:c:p:103-115
    DOI: 10.1016/j.jmva.2017.02.002
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    References listed on IDEAS

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    1. Tran, Lanh Tat, 1990. "Kernel density estimation on random fields," Journal of Multivariate Analysis, Elsevier, vol. 34(1), pages 37-53, July.
    2. Marc Hallin & Zudi Lu & Lanh T. Tran, 2004. "Local linear spatial regression," ULB Institutional Repository 2013/2131, ULB -- Universite Libre de Bruxelles.
    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. Lu, Zudi & Chen, Xing, 2004. "Spatial kernel regression estimation: weak consistency," Statistics & Probability Letters, Elsevier, vol. 68(2), pages 125-136, June.
    5. Wang, Yizao & Woodroofe, Michael, 2014. "On the asymptotic normality of kernel density estimators for causal linear random fields," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 201-213.
    6. Gérard Biau & Benoît Cadre, 2004. "Nonparametric Spatial Prediction," Statistical Inference for Stochastic Processes, Springer, vol. 7(3), pages 327-349, October.
    7. Kulkarni, P. M., 1992. "Estimation of parameters of a two-dimensional spatial autoregressive model with regression," Statistics & Probability Letters, Elsevier, vol. 15(2), pages 157-162, September.
    8. Marc Hallin & Zudi Lu & Lanh T. Tran, 2001. "Density estimation for spatial linear processes," ULB Institutional Repository 2013/2109, ULB -- Universite Libre de Bruxelles.
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    Cited by:

    1. Kurisu, Daisuke, 2019. "On nonparametric inference for spatial regression models under domain expanding and infill asymptotics," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
    2. Palle Jorgensen & Feng Tian, 2019. "Realizations and Factorizations of Positive Definite Kernels," Journal of Theoretical Probability, Springer, vol. 32(4), pages 1925-1942, December.

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