Nonparametric identification of the spatial autoregression model under a priori stochastic uncertainty

For the process of spatial autoregression of the order $(1,1)$, constructed were the locally most powerful sign criteria for verification of the hypotheses about the coefficients of the autoregression equation in the conditions where the distribution of the innovative process was unknown. The statistics of criteria are free of distribution; their asymptotic normality was proved. An algorithm to construct the point estimates of the coefficients of the autoregression equation was proposed on the basis of the statistics of the sign criteria. The assumptions about the innovative sequence of autoregression are rather weak and do not require finiteness of variance or evenness of density. All methods are stable to the observation “overshoots”.