On dealing with spatially correlated residuals in remote sensing and GIS

Key assumptions in standard regression models are that the residuals are independent and identically distributed. These assumptions are often not met in practice. In particular, the issue of spatial correlation amongst the residuals has had limited attention in the remote sensing and GIS literature. This paper discusses approaches that use familiar authorized models to specify the covariance amongst the residuals. The model parameters were estimated using a maximum likelihood approach (ML or REML). The accuracy of the approach was investigated using simulated data and found to give accurate estimates of the error variance (σ²), although estimates of and range (a) and nugget component (s) were less accurate. The approach was found to be robust to choice of covariance function (exponential or spherical). The approach was then extended to deal with heteroskedastic residuals by incorporating a weighting component analogous to that used in weighted least squares. This was also shown to yield accurate results for σ², a and s. Finally, possibilities for extending these approaches to prediction are considered.