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Estimation of parameters of a two-dimensional spatial autoregressive model with regression

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  • Kulkarni, P. M.

Abstract

A two-dimensional autoregressive model with regression has been considered in its causal form using the representation of Basawa, Brockwell and Mandrekar (1990). Asymptotic normality of the estimators of the parameters is derived. Further, an Empirical Bayes estimator is suggested for the regression coefficient. It is shown that the asymptotic risk of this Empirical Bayes estimator is less than that of the maximum likelihood estimator. These findings are in accordance with Kim, Nickerson and Basawa (1989).

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:15:y:1992:i:2:p:157-162
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    Cited by:

    1. Hallin, Marc & Lu, Zudi & Tran, Lanh T., 2004. "Kernel density estimation for spatial processes: the L1 theory," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 61-75, January.
    2. Lu, Zudi & Chen, Xing, 2004. "Spatial kernel regression estimation: weak consistency," Statistics & Probability Letters, Elsevier, vol. 68(2), pages 125-136, June.
    3. 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.
    4. Michel Carbon, 2014. "Histograms for stationary linear random fields," Statistical Inference for Stochastic Processes, Springer, vol. 17(3), pages 245-266, October.

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