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Bayesian Local Influence for Spatial Autoregressive Models with Heteroscedasticity

Author

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  • Xiaowen Dai

    (Shanghai Lixin University of Accounting and Finance)

  • Libin Jin

    (Shanghai Lixin University of Accounting and Finance)

  • Maozai Tian

    (Renmin University of China)

  • Lei Shi

    (Yunnan University of Finance and Economics)

Abstract

This paper studies Bayesian local influence analysis for the spatial autoregressive models with heteroscedasticity (heteroscedastic SAR models). Two local diagnostic procedures using curvature-based and slope-based methods are proposed in the framework of Bayesian perspective. The curvature-based diagnostic are obtained by maximizing the normal curvature of an influence graph based on Kullback–Leibler divergence measure and slope-based diagnostic use the first order derivative of Bayesian factor defined for perturbation. Three perturbation schemes under the heteroscedastic SAR models are suggested and the diagnostic measures are derived respectively. The computations for the proposed diagnostic measures can be easily obtained using Markov Chain Monte Carlo sampler. The proposed methodologies are illustrated using two real examples.

Suggested Citation

  • Xiaowen Dai & Libin Jin & Maozai Tian & Lei Shi, 2019. "Bayesian Local Influence for Spatial Autoregressive Models with Heteroscedasticity," Statistical Papers, Springer, vol. 60(5), pages 1423-1446, October.
    • Handle: RePEc:spr:stpapr:v:60:y:2019:i:5:d:10.1007_s00362-017-0880-1
    DOI: 10.1007/s00362-017-0880-1
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    References listed on IDEAS

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    1. Manuel Galea & Gilberto Paula & Miguel Uribe-Opazo, 2003. "On influence diagnostic in univariate elliptical linear regression models," Statistical Papers, Springer, vol. 44(1), pages 23-45, January.
    2. Hong‐Tu Zhu & Sik‐Yum Lee, 2001. "Local influence for incomplete data models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(1), pages 111-126.
    3. Patricia Giménez & María Patat, 2014. "Local influence for functional comparative calibration models with replicated data," Statistical Papers, Springer, vol. 55(2), pages 431-454, May.
    4. Libin Jin & Xiaowen Dai & Anqi Shi & Lei Shi, 2016. "Detection of outliers in mixed regressive-spatial autoregressive models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(17), pages 5179-5192, September.
    5. Xiaowen Dai & Libin Jin & Anqi Shi & Lei Shi, 2016. "Outlier detection and accommodation in general spatial models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(3), pages 453-475, August.
    6. V. Lachos & T. Angolini & C. Abanto-Valle, 2011. "On estimation and local influence analysis for measurement errors models under heavy-tailed distributions," Statistical Papers, Springer, vol. 52(3), pages 567-590, August.
    7. Camila Zeller & Victor Lachos & Filidor Labra, 2014. "Influence diagnostics for Grubbs’s model with asymmetric heavy-tailed distributions," Statistical Papers, Springer, vol. 55(3), pages 671-690, August.
    8. Fukang Zhu & Lei Shi & Shuangzhe Liu, 2015. "Influence diagnostics in log-linear integer-valued GARCH models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(3), pages 311-335, July.
    9. W.‐Y. Poon & Y. S. Poon, 1999. "Conformal normal curvature and assessment of local influence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 51-61.
    10. Lei Shi & Md. Mostafizur Rahman & Wen Gan & Jianhua Zhao, 2015. "Stepwise local influence in generalized autoregressive conditional heteroskedasticity models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(2), pages 428-444, February.
    11. Hongtu Zhu & Joseph G. Ibrahim & Niansheng Tang, 2011. "Bayesian influence analysis: a geometric approach," Biometrika, Biometrika Trust, vol. 98(2), pages 307-323.
    12. Pan, Jian-Xin & Fang, Kai-Tai & Liski, Erkki P., 1996. "Bayesian Local Influence for the Growth Curve Model with Rao's Simple Covariance Structure," Journal of Multivariate Analysis, Elsevier, vol. 58(1), pages 55-81, July.
    13. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    14. Shi, Lei & Huang, Mei, 2011. "Stepwise local influence analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 973-982, February.
    15. Krnjajić, Milovan & Draper, David, 2014. "Bayesian model comparison: Log scores and DIC," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 9-14.
    16. Xiaowen Dai & Libin Jin & Lei Shi & Cuiping Yang & Shuangzhe Liu, 2016. "Local influence analysis in general spatial models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(3), pages 313-331, July.
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