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Shrinkage estimation of the linear model with spatial interaction

Author

Listed:
  • Yueqin Wu

    (Shanghai Normal University)

  • Yan Sun

    (Shanghai University of Finance and Economics)

Abstract

The linear model with spatial interaction has attracted huge attention in the past several decades. Different from most existing research which focuses on its estimation, we study its variable selection problem using the adaptive lasso. Our results show that the method can identify the true model consistently, and the resulting estimator can be efficient as the oracle estimator which is obtained when the zero coefficients in the model are known. Simulation studies show that the proposed methods perform very well.

Suggested Citation

  • Yueqin Wu & Yan Sun, 2017. "Shrinkage estimation of the linear model with spatial interaction," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(1), pages 51-68, January.
    • Handle: RePEc:spr:metrik:v:80:y:2017:i:1:d:10.1007_s00184-016-0590-z
    DOI: 10.1007/s00184-016-0590-z
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    References listed on IDEAS

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    1. Kelejian, Harry H & Prucha, Ingmar R, 1999. "A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(2), pages 509-533, May.
    2. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    3. Kelejian, Harry H & Prucha, Ingmar R, 1998. "A Generalized Spatial Two-Stage Least Squares Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbances," The Journal of Real Estate Finance and Economics, Springer, vol. 17(1), pages 99-121, July.
    4. Kelejian, Harry H. & Prucha, Ingmar R., 2010. "Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances," Journal of Econometrics, Elsevier, vol. 157(1), pages 53-67, July.
    5. Zhang, Yiyun & Li, Runze & Tsai, Chih-Ling, 2010. "Regularization Parameter Selections via Generalized Information Criterion," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 312-323.
    6. Lee, Lung-fei, 2007. "The method of elimination and substitution in the GMM estimation of mixed regressive, spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 140(1), pages 155-189, September.
    7. Su, Liangjun & Jin, Sainan, 2010. "Profile quasi-maximum likelihood estimation of partially linear spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 157(1), pages 18-33, July.
    8. Smirnov, Oleg & Anselin, Luc, 2001. "Fast maximum likelihood estimation of very large spatial autoregressive models: a characteristic polynomial approach," Computational Statistics & Data Analysis, Elsevier, vol. 35(3), pages 301-319, January.
    9. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    10. Case, Anne C, 1991. "Spatial Patterns in Household Demand," Econometrica, Econometric Society, vol. 59(4), pages 953-965, July.
    11. Wang, Hansheng & Xia, Yingcun, 2009. "Shrinkage Estimation of the Varying Coefficient Model," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 747-757.
    12. Lung-Fei Lee, 2004. "Asymptotic Distributions of Quasi-Maximum Likelihood Estimators for Spatial Autoregressive Models," Econometrica, Econometric Society, vol. 72(6), pages 1899-1925, November.
    13. Lee, Lung-fei, 2007. "GMM and 2SLS estimation of mixed regressive, spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 137(2), pages 489-514, April.
    14. Lung-fei Lee, 2003. "Best Spatial Two-Stage Least Squares Estimators for a Spatial Autoregressive Model with Autoregressive Disturbances," Econometric Reviews, Taylor & Francis Journals, vol. 22(4), pages 307-335.
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    Cited by:

    1. Tizheng Li & Xiaojuan Kang, 2022. "Variable selection of higher-order partially linear spatial autoregressive model with a diverging number of parameters," Statistical Papers, Springer, vol. 63(1), pages 243-285, February.
    2. Fang Lu & Jing Yang & Xuewen Lu, 2022. "One-step oracle procedure for semi-parametric spatial autoregressive model and its empirical application to Boston housing price data," Empirical Economics, Springer, vol. 62(6), pages 2645-2671, June.
    3. Liu, Yu & Zhuang, Xiaoyang, 2023. "Shrinkage estimation of semi-parametric spatial autoregressive panel data model with fixed effects," Statistics & Probability Letters, Elsevier, vol. 194(C).

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