Statistical hypotheses testing for parameters of binomial conditionally autoregressive model of spatio-temporal data

This paper is devoted to new binomial conditional autoregressive model of spatio-temporal data. This model is multidimensional non-homogeneous Markov chain with a finite state space. We use the maximum likelihood method for statistical estimation of the model parameters. We show that these estimators are consistent and asymptotically normally distributed. Fisher information matrix is calculated; it takes block-diagonal form and is nonsingular. The results of the analysis of the asymptotic properties of the maximum likelihood estimators are used to construct a statistic for statistical testing of hypotheses about the values of the parameters of the binomial conditional autoregressive model. Decision rule for statistical hypotheses testing is built and an asymptotic expression of the power of the test is obtained for a family of contiguous alternatives. Experiments have been conducted on simulated data to evaluate performance of the constructed decision rule. Plots of experimental and theoretical estimates of the first type error probability and power of the test in dependence on the length of the observation period are presented, they illustrate adequacy of theoretical and experimental results.