IDEAS home Printed from https://ideas.repec.org/a/spr/empeco/v62y2022i6d10.1007_s00181-021-02118-z.html
   My bibliography  Save this article

One-step oracle procedure for semi-parametric spatial autoregressive model and its empirical application to Boston housing price data

Author

Listed:
  • Fang Lu

    (Hunan Normal University)

  • Jing Yang

    (Hunan Normal University)

  • Xuewen Lu

    (University of Calgary)

Abstract

Issues concerning spatial dependence among cross-sectional units in econometrics have received more and more attention. Motivated by a Boston housing price data analysis, this paper studies the sparse inference of varying coefficient partially linear spatial autoregressive model, which is quite valuable in econometrics with high-dimensional data. A novel, efficient and convenient one-step variable selection procedure is proposed by using a twofold penalty for simultaneous estimation and variable selection of the parametric components and varying coefficient functions, in which the varying coefficient functions are approximated by the B-spline basis. Under some regularity conditions, asymptotic properties of the resulting estimators are established, including consistency, asymptotic normality and the oracle property. Besides, the optimal choices of the tuning parameters are discussed and a practical iterative algorithm based on the locally quadratic approximation approach is presented for implementation. Finally, extensive numerical simulations and a Boston housing price data analysis are conducted to confirm the finite sample performance and theoretical findings of the new method.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:empeco:v:62:y:2022:i:6:d:10.1007_s00181-021-02118-z
    DOI: 10.1007/s00181-021-02118-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00181-021-02118-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00181-021-02118-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Heng Lian, 2012. "Semiparametric Estimation of Additive Quantile Regression Models by Two-Fold Penalty," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(3), pages 337-350, March.
    2. Chunrong Ai & Yuanqing Zhang, 2017. "Estimation of partially specified spatial panel data models with fixed-effects," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 6-22, March.
    3. Xu, Xingbai & Lee, Lung-fei, 2015. "A spatial autoregressive model with a nonlinear transformation of the dependent variable," Journal of Econometrics, Elsevier, vol. 186(1), pages 1-18.
    4. Su, Liangjun, 2012. "Semiparametric GMM estimation of spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 167(2), pages 543-560.
    5. Pace, R Kelley & Gilley, Otis W, 1997. "Using the Spatial Configuration of the Data to Improve Estimation," The Journal of Real Estate Finance and Economics, Springer, vol. 14(3), pages 333-340, May.
    6. 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.
    7. Noh, Hohsuk & Chung, Kwanghun & Van Keilegom, Ingrid, 2012. "Variable selection of varying coefficient models in quantile regression," LIDAM Reprints ISBA 2012008, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Lin, Xu & Lee, Lung-fei, 2010. "GMM estimation of spatial autoregressive models with unknown heteroskedasticity," Journal of Econometrics, Elsevier, vol. 157(1), pages 34-52, July.
    9. 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.
    10. Tianfa Xie & Ruiyuan Cao & Jiang Du, 2020. "Variable selection for spatial autoregressive models with a diverging number of parameters," Statistical Papers, Springer, vol. 61(3), pages 1125-1145, June.
    11. Yang, Zhenlin & Li, Chenwei & Tse, Y.K., 2006. "Functional form and spatial dependence in dynamic panels," Economics Letters, Elsevier, vol. 91(1), pages 138-145, April.
    12. Noh, Hohsuk & Chung, Kwanghun & Van Keilegom, Ingrid, 2012. "Variable Selection of Varying Coefficient Models in Quantile Regression," LIDAM Discussion Papers ISBA 2012020, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    13. Yan Sun & Yueqin Wu, 2018. "Estimation and testing for a partially linear single-index spatial regression model," Spatial Economic Analysis, Taylor & Francis Journals, vol. 13(4), pages 473-489, October.
    14. Roberto BASILE & Bernard GRESS, 2005. "Semi-Parametric Spatial Auto-Covariance Models Of Regional Growth In Europe," Region et Developpement, Region et Developpement, LEAD, Universite du Sud - Toulon Var, vol. 21, pages 93-118.
    15. 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.
    16. Philip Kostov, 2009. "A Spatial Quantile Regression Hedonic Model of Agricultural Land Prices," Spatial Economic Analysis, Taylor & Francis Journals, vol. 4(1), pages 53-72.
    17. 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.
    18. 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.
    19. Wang, Dewei & Kulasekera, K.B., 2012. "Parametric component detection and variable selection in varying-coefficient partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 117-129.
    20. 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.
    21. 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.
    22. Wei, Chuanhua & Guo, Shuang & Zhai, Shufen, 2017. "Statistical inference of partially linear varying coefficient spatial autoregressive models," Economic Modelling, Elsevier, vol. 64(C), pages 553-559.
    23. Badi H. Baltagi & Dong Li, 2001. "LM Tests for Functional Form and Spatial Error Correlation," International Regional Science Review, , vol. 24(2), pages 194-225, April.
    24. Sun, Yanqing & Zhang, Yuanqing & Huang, Jianhua Z., 2019. "Estimation of a semiparametric varying-coefficient mixed regressive spatial autoregressive model," Econometrics and Statistics, Elsevier, vol. 9(C), pages 140-155.
    25. Harrison, David Jr. & Rubinfeld, Daniel L., 1978. "Hedonic housing prices and the demand for clean air," Journal of Environmental Economics and Management, Elsevier, vol. 5(1), pages 81-102, March.
    26. Chen, Yixin & Wang, Qin & Yao, Weixin, 2015. "Adaptive estimation for varying coefficient models," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 17-31.
    27. Peixin Zhao & Liugen Xue, 2012. "Variable selection in semiparametric regression analysis for longitudinal data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(1), pages 213-231, February.
    28. 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.
    29. Yingcun Xia, 2004. "Efficient estimation for semivarying-coefficient models," Biometrika, Biometrika Trust, vol. 91(3), pages 661-681, September.
    30. Pal, Amresh Bahadur & Dubey, Ashutosh Kumar & Chaturvedi, Anoop, 2016. "Shrinkage estimation in spatial autoregressive model," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 362-373.
    31. 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.
    32. Zhang, Hao Helen & Cheng, Guang & Liu, Yufeng, 2011. "Linear or Nonlinear? Automatic Structure Discovery for Partially Linear Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1099-1112.
    33. 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.
    34. Sun, Yan, 2017. "Estimation of single-index model with spatial interaction," Regional Science and Urban Economics, Elsevier, vol. 62(C), pages 36-45.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Zhengyu Zhang, 2013. "A Pairwise Difference Estimator for Partially Linear Spatial Autoregressive Models," Spatial Economic Analysis, Taylor & Francis Journals, vol. 8(2), pages 176-194, June.
    3. Tianfa Xie & Ruiyuan Cao & Jiang Du, 2020. "Variable selection for spatial autoregressive models with a diverging number of parameters," Statistical Papers, Springer, vol. 61(3), pages 1125-1145, June.
    4. 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.
    5. Malikov, Emir & Sun, Yiguo, 2017. "Semiparametric estimation and testing of smooth coefficient spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 199(1), pages 12-34.
    6. Jiawei Hou & Yunquan Song, 2022. "Interquantile shrinkage in spatial additive autoregressive models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 1030-1057, December.
    7. Luo, Guowang & Wu, Mixia & Pang, Zhen, 2022. "Estimation of spatial autoregressive models with covariate measurement errors," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    8. Zhang, Xinyu & Yu, Jihai, 2018. "Spatial weights matrix selection and model averaging for spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 203(1), pages 1-18.
    9. Liangjun Su & Xi Qu, 2017. "Specification Test for Spatial Autoregressive Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(4), pages 572-584, October.
    10. Yang, Zhenlin, 2015. "A general method for third-order bias and variance corrections on a nonlinear estimator," Journal of Econometrics, Elsevier, vol. 186(1), pages 178-200.
    11. Zhiyong Chen & Jianbao Chen, 2022. "Bayesian analysis of partially linear, single-index, spatial autoregressive models," Computational Statistics, Springer, vol. 37(1), pages 327-353, March.
    12. Jin, Fei & Lee, Lung-fei, 2013. "Cox-type tests for competing spatial autoregressive models with spatial autoregressive disturbances," Regional Science and Urban Economics, Elsevier, vol. 43(4), pages 590-616.
    13. 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).
    14. Yunquan Song & Hang Su & Minmin Zhan, 2024. "Local Walsh-average-based Estimation and Variable Selection for Spatial Single-index Autoregressive Models," Networks and Spatial Economics, Springer, vol. 24(2), pages 313-339, June.
    15. Kwok, Hon Ho, 2019. "Identification and estimation of linear social interaction models," Journal of Econometrics, Elsevier, vol. 210(2), pages 434-458.
    16. Wei, Chuanhua & Guo, Shuang & Zhai, Shufen, 2017. "Statistical inference of partially linear varying coefficient spatial autoregressive models," Economic Modelling, Elsevier, vol. 64(C), pages 553-559.
    17. Xuan Liu & Jianbao Chen, 2021. "Variable Selection for the Spatial Autoregressive Model with Autoregressive Disturbances," Mathematics, MDPI, vol. 9(12), pages 1-20, June.
    18. Doğan, Osman & Taşpınar, Süleyman, 2014. "Spatial autoregressive models with unknown heteroskedasticity: A comparison of Bayesian and robust GMM approach," Regional Science and Urban Economics, Elsevier, vol. 45(C), pages 1-21.
    19. Sun, Yan, 2017. "Estimation of single-index model with spatial interaction," Regional Science and Urban Economics, Elsevier, vol. 62(C), pages 36-45.
    20. Zhang Yuanqing, 2014. "Estimation of Partially Specified Spatial Autoregressive Model," Journal of Systems Science and Information, De Gruyter, vol. 2(3), pages 226-235, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:empeco:v:62:y:2022:i:6:d:10.1007_s00181-021-02118-z. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.