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

ýRecently a first-order Spatial Integer-valued Autoregressiveý ýSINAR(1,1) model was introduced to model spatial data that comesý ýin counts citep{ghodsi2012}ý. ýSome properties of this modelý ýhave been established and the Yule-Walker estimator has beený ýproposed for this modelý. ýIn this paperý, ýwe introduce theý ýconditional maximum likelihood method for estimating theý ýparameters of the Poisson SINAR(1,1) modelý. ýThe asymptoticý ýdistribution of the estimators are also derivedý. ýThe properties ofý ýthe Yule-Walker and conditional maximum likelihood estimators areý ýcompared by simulation studyý. ýFinallyý, ýthe Student data citep{student1906} oný ýthe yeast cells count are used to illustrate the fitting of theý ýSINAR(1,1) modelý.