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The multilateral spatial integer‐valued process of order 1

Author

Listed:
  • Dimitris Karlis
  • Azmi Chutoo
  • Naushad Mamode Khan
  • Vandna Jowaheer

Abstract

In spatial count data analysis, modeling with a multilateral lattice structure presents some important challenges. They include both the model construction and the estimation of the model parameters, since the structure accommodates the left, right, top, bottom, and diagonal site effects. Thus, the multilateral spatial process unifies all the popular spatial subclasses that include the unilateral, Rook, Bishop, and Queen models and, hence, makes it suitable for a wide variety of applications. This paper introduces a first‐order multilateral integer‐valued spatial process, based on a binomial thinning mechanism and some innovation term, under both stationary and nonstationary conditions. The estimation of parameters is handled by the conditional maximum likelihood estimation (CML) approach. Simulation experiments are implemented to assess the consistency of the CML estimators in the stationary and nonstationary multilateral spatial model and its subclasses, based on different grid sizes and under both covariate and noncovariate designs. The proposed model, along with its subclasses are applied to real datasets.

Suggested Citation

  • Dimitris Karlis & Azmi Chutoo & Naushad Mamode Khan & Vandna Jowaheer, 2024. "The multilateral spatial integer‐valued process of order 1," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 78(1), pages 4-24, February.
    • Handle: RePEc:bla:stanee:v:78:y:2024:i:1:p:4-24
    DOI: 10.1111/stan.12298
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    References listed on IDEAS

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    1. Ruijun Bu & Kaddour Hadri & Brendan McCabe, 2006. "Conditional Maximum Likelihood Estimation of Higher-Order Integer-Valued Autoregressive Processes," Working Papers 200619, University of Liverpool, Department of Economics.
    2. Luc Anselin & Rodolfo Bongiovanni & Jess Lowenberg-DeBoer, 2004. "A Spatial Econometric Approach to the Economics of Site-Specific Nitrogen Management in Corn Production," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 86(3), pages 675-687.
    3. Hååvard Rue & Hååkon Tjelmeland, 2002. "Fitting Gaussian Markov Random Fields to Gaussian Fields," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(1), pages 31-49, March.
    4. Pace, R Kelley & Gilley, Otis W, 1997. "Using the Spatial Configuration of the Data to Improve Estimation," The Journal of Real Estate Finance and Economics, Springer, vol. 14(3), pages 333-340, May.
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    Cited by:

    1. Christian H. Weiß & Hee-Young Kim, 2025. "Non-parametric entropy tests for spatial dependence," Computational Statistics, Springer, vol. 40(9), pages 5315-5352, December.

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