Conditional Maximum Likelihood Estimation of the First-Order Spatial Non-Negative Integer-Valued Autoregressive (SINAR(1,1)) Model

Recently a first-order Spatial Integer-valued Autoregressive SINAR(1,1) model was introduced to model spatial data that comes in counts (Ghodsi et al., 2012). Some properties of this model have been established and the Yule-Walker estimator has been proposed for this model. In this paper, we introduce the conditional maximum likelihood method for estimating the parameters of the Poisson SINAR(1,1) model. The asymptotic distribution of the estimators are also derived. The properties of the Yule-Walker and conditional maximum likelihood estimators are compared by simulation study. Finally, the Student data (Student, 1906) on the yeast cells count are used to illustrate the fitting of the SINAR(1,1) model.