Inference for Spatial Autoregressive Models with Infinite Variance Noises

• 作者: Gui Li LIAO Qi Meng LIU Rong Mao ZHANG
• 来源期刊: 数学学报（英文版）
• 年，卷（期）: 2020,（12）
• 页码范围: 1395-1416
• 页数: 22页
• 语种: 英文

摘要

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 chi-squared distribution. Simulations and a real data example are also reported to assess the performance of the proposed method.