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Inference for Spatial Autoregressive Models with Infinite Variance Noises

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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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Acknowledgements

We would like to thank the Editor, the Co-Editor, and the anonymous referees for their critical comments and thoughtful suggestions, which lead to a much improved version of this paper.

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Authors and Affiliations

  1. School of Mathematical Science, Zhejiang University, Hangzhou, 310027, P.R. China

    Gui Li Liao, Qi Meng Liu & Rong Mao Zhang

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  1. Gui Li Liao
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  2. Qi Meng Liu
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  3. Rong Mao Zhang
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Correspondence to Qi Meng Liu.

Additional information

Supported by NSFC (Grant Nos. 11771390 and 11371318), Zhejiang Provincial Natural Science Foundation of China (Grant No. LR16A010001) and the Fundamental Research Funds for the Central Universities 1) Corresponding author

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Liao, G.L., Liu, Q.M. & Zhang, R.M. Inference for Spatial Autoregressive Models with Infinite Variance Noises. Acta. Math. Sin.-English Ser. 36, 1395–1416 (2020). https://doi.org/10.1007/s10114-020-9428-8

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  • DOI: https://doi.org/10.1007/s10114-020-9428-8

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