Author

• A. Ghodsi

Department of Statistics, Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran.

Abstract

‎Recently a first-order Spatial Integer-valued Autoregressive‎ ‎SINAR(1,1) model was introduced to model spatial data that comes‎ ‎in counts citep < /span>{ghodsi2012}‎. ‎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 citep < /span>{student1906} on‎ ‎the yeast cells count are used to illustrate the fitting of the‎ ‎SINAR(1,1) model‎.

Keywords

• SINAR(1
• 1) model
• Spatial integer-valued autoregressive model
• Conditional maximum likelihood estimation
• Binomial thinning operator