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

Authors:
Johan Lim;Kiseop Lee;Donghyeon Yu;Haiyan Liu;Michael Sherman
Affiliations:
Department of Statistics, Seoul National University, Seoul, 151-747, Republic of Korea;Department of Mathematics, University of Louisville, Louisville, KY 40292, USA and Graduate Department of Financial Engineering, Ajou University, Suwon, Republic of Korea;Department of Statistics, Seoul National University, Seoul, 151-747, Republic of Korea;Sunnyvale, CA, USA;Department of Statistics, Texas A&M University, College Station, TX 77843-3143, USA
Venue:
Computational Statistics & Data Analysis
Year:
2012

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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.