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Keywords:

  • Spatial autoregression;
  • maximum likelihood estimation;
  • quasi-maximum likelihood estimator;
  • rates of convergence;
  • increasing-domain asymptotics;
  • infill asymptotics

This paper investigates asymptotic properties of the maximum likelihood estimator and the quasi-maximum likelihood estimator for the spatial autoregressive model. The rates of convergence of those estimators may depend on some general features of the spatial weights matrix of the model. It is important to make the distinction with different spatial scenarios. Under the scenario that each unit will be influenced by only a few neighboring units, the estimators may have inline image-rate of convergence and be asymptotically normal. When each unit can be influenced by many neighbors, irregularity of the information matrix may occur and various components of the estimators may have different rates of convergence.