QML estimation with non-summable weight matrices

This paper revisits the theory of asymptotic behaviour of the well-known Gaussian Quasi-Maximum Likelihood estimator of parameters in mixed regressive, high-order autoregressive spatial models. We generalise the approach previously published in the econometric literature by weakening the assumptions imposed on the spatial weight matrix. This allows consideration of interaction patterns with a potentially larger degree of spatial dependence. Moreover, we broaden the class of admissible distributions of model residuals. As an example application of our new asymptotic analysis we also consider the large sample behaviour of a general group effects design.