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Parameter estimation in the spatial auto-logistic model with working independent subblocks

Author

Listed:
  • Lim, Johan
  • Lee, Kiseop
  • Yu, Donghyeon
  • Liu, Haiyan
  • Sherman, Michael

Abstract

We propose an approximation to the likelihood function with independent sub-blocks in the spatial auto-logistic model. The entire data is subdivided into many sub-blocks which are treated as independent from each other. The approximate maximum likelihood estimator, called maximum block independent likelihood estimator, is shown to have the same asymptotic distribution as that of the maximum likelihood estimator in the Ising model, a special case of the spatial auto-logistic model. The computational load for the proposed estimator is much lighter than that for the maximum likelihood estimator, and decreases geometrically as the size of a sub-block decreases. Also, limited simulation studies show that, in finite samples, the maximum block independent likelihood estimator performs as well as the maximum likelihood estimator in mean squared error. We apply our procedure to an estimation and a test of spatial dependence in the longleaf pine tree data in Cressie (1993) and the aerial image data in Pyun et al. (2007). Finally, we discuss the extension of the proposed estimator to other spatial auto-regressive models.

Suggested Citation

  • Lim, Johan & Lee, Kiseop & Yu, Donghyeon & Liu, Haiyan & Sherman, Michael, 2012. "Parameter estimation in the spatial auto-logistic model with working independent subblocks," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4421-4432.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:12:p:4421-4432
    DOI: 10.1016/j.csda.2012.03.013
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    References listed on IDEAS

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    1. Caragea, Petruta C. & Smith, Richard L., 2007. "Asymptotic properties of computationally efficient alternative estimators for a class of multivariate normal models," Journal of Multivariate Analysis, Elsevier, vol. 98(7), pages 1417-1440, August.
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