A self-weighted quantile procedure is proposed to study the inference for a spatial unilateral autoregressive model with independent and identically distributed innovations belonging to the domain of attraction of a stable law with index of stability α, α ∈ (0, 2]. It is shown that when the model is stationary, the self-weighted quantile estimate of the parameter has a closed form and converges to a normal limiting distribution, which avoids the difficulty of Roknossadati and Zarepour (2010) in deriving their limiting distribution for an M-estimate. On the contrary, we show that when the model is not stationary, the proposed estimates have the same limiting distributions as those of Roknossadati and Zarepour. Furthermore, a Wald test statistic is proposed to consider the test for a linear restriction on the parameter, and it is shown that under a local alternative, the Wald statistic has a non-central chisquared distribution. Simulations and a real data example are also reported to assess the performance of the proposed method.

提出了一种自加权分位数程序，以研究具有独立且均匀分布的创新的空间单边自回归模型的推论，该创新属于具有稳定指数α，α的稳定定律的吸引域∈（0，2]。研究表明，当模型稳定时，参数的自加权分位数估计具有封闭形式，并收敛于正态极限分布，从而避免了Roknossadati和Zarepour（2010）的困难。相反，我们表明，当模型不是平稳的时，建议的估计具有与Roknossadati和Zarepour相同的极限分布，此外，还提出了Wald检验统计量来考虑检验参数的线性限制，结果表明，在局部选择下，Wald统计量具有非中心卡方分布，并且还报告了仿真和实际数据示例，以评估该方法的性能。