M-estimation for near unit roots in spatial autoregression with infinite variance

We investigate the limiting behaviour of M-estimators of parameters for a near unit root spatial autoregressive model Z(ij) (n) = alpha(n)Z(i-1,) (j) (n) + beta(n)Z(i, j-1)(n) - alpha(n)beta(n)Z(i-1, j-1)(n) + epsilon(ij), 1 <= i, j <= n. Innovations are assumed to be independent and identically distributed and in the domain of attraction of a stable law. We let alpha(n) = e(c/n) and beta(n) = e(d/n), where c and d are nonzero unknown constants. It is shown that the self-normalized M-estimators are asymptotically normal. A simulation study is also given.