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- Title
Inference for Spatial Autoregressive Models with Infinite Variance Noises.
- Authors
Liao, Gui Li; Liu, Qi Meng; Zhang, Rong Mao
- 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.
- Subjects
AUTOREGRESSIVE models; VARIANCES; GAUSSIAN distribution; NOISE; QUANTILE regression
- Publication
Acta Mathematica Sinica, 2020, Vol 36, Issue 12, p1395
- ISSN
1439-8516
- Publication type
Article
- DOI
10.1007/s10114-020-9428-8