ESTIMATION OF LINEAR CORRELATION COEFFICIENT OF TWO CORRELATED SPATIAL PROCESSES

Standard inferential methods for the correlation coefficient for two normally distributed variables are based on the assumption of independent sampling. In general, this assumption is not appropriate for spatial data where contiguous locations exhibit some significant level of spatial-correlation or autocorrelation. Past works have demonstrated the dangers, in the form of underestimated standard errors and inflated Type I errors, of applying independent-sample inference methods on spatially correlated data. Here, we study the distribution of maximum likelihood estimators in a bivariate spatial model and give the finite sample distribution and asymptotic distribution of estimators. We show that if the estimator appropriately accounts for spatial correlation, some existing distributional results derived under the assumption of independence are still valid.