Inference for Spatial Autoregressive Models with Infinite Variance Noises |
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Authors: | Gui Li LIAO Qi Meng LIU Rong Mao ZHANG |
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Affiliation: | School of Mathematical Science, Zhejiang University, Hangzhou 310027, P. R. China |
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Abstract: | 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. |
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Keywords: | Spatial autoregressive model heavy-tailed noise self-weighted quantile inference Wald statistic |
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