IDEAS home Printed from https://ideas.repec.org/a/kap/netspa/v24y2024i2d10.1007_s11067-024-09616-4.html
   My bibliography  Save this article

Local Walsh-average-based Estimation and Variable Selection for Spatial Single-index Autoregressive Models

Author

Listed:
  • Yunquan Song

    (China University of Petroleum)

  • Hang Su

    (China University of Petroleum)

  • Minmin Zhan

    (China University of Petroleum)

Abstract

This paper is concerned with spatial single-index autoregressive model (SSIM), where the spatial lag effect enters the model linearly and the relationship between variables is a nonparametric function of a linear combination of multivariate regressors. It addresses challenges related to the curse of dimensionality and interactions among non-independent variables in spatial data. The local Walsh-average regression has proven to be a robust and efficient method for handling single-index models. We extend this approach to the spatial domain, propose a regularized local Walsh-average (RLWA) estimation strategy where the nonparametric component is established by a local Walsh-average approach and the estimation of the parametric part by Walsh-average method. Under specific assumptions, we establish the asymptotic properties of both parametric and nonparametric partial estimators. Additionally, we propose a robust shrinkage method termed regularized local Walsh-average (RLWA) that can construct robust parametric variable selection and robust nonparametric component estimation simultaneously. Theoretical analysis reveals RLWA works beautifully, including consistency in variable selection and oracle property in estimation. We propose a parameter selection process based on a robust BIC-type approach with an oracle property. The effectiveness of the proposed estimation procedure is evaluated through three Monte Carlo simulations and real data applications, demonstrating its performance in finite samples.

Suggested Citation

  • 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.
    • Handle: RePEc:kap:netspa:v:24:y:2024:i:2:d:10.1007_s11067-024-09616-4
    DOI: 10.1007/s11067-024-09616-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11067-024-09616-4
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11067-024-09616-4?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. Wang, Hai-Bin, 2009. "Bayesian estimation and variable selection for single index models," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2617-2627, May.
    2. Su, Liangjun, 2012. "Semiparametric GMM estimation of spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 167(2), pages 543-560.
    3. Feng, Long & Zou, Changliang & Wang, Zhaojun, 2012. "Local Walsh-average regression," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 36-48.
    4. Li-Ping Zhu & Lin-Yi Qian & Jin-Guan Lin, 2011. "Variable selection in a class of single-index models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(6), pages 1277-1293, December.
    5. Yunquan Song & Zitong Li & Minglu Fang, 2022. "Robust Variable Selection Based on Penalized Composite Quantile Regression for High-Dimensional Single-Index Models," Mathematics, MDPI, vol. 10(12), pages 1-17, June.
    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. Zhao, Weihua & Zhou, Yan & Lian, Heng, 2018. "Time-varying quantile single-index model for multivariate responses," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 32-49.
    8. 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.
    9. Terpstra, Jeff T. & McKean, Joseph W., 2005. "Rank-Based Analysis of Linear Models Using R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 14(i07).
    10. Wang, Lan & Kai, Bo & Li, Runze, 2009. "Local Rank Inference for Varying Coefficient Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1631-1645.
    11. 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.
    12. Zhao, Weihua & Jiang, Xuejun & Lian, Heng, 2018. "A principal varying-coefficient model for quantile regression: Joint variable selection and dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 269-280.
    13. 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.
    14. Roberto Basile, 2008. "Regional economic growth in Europe: A semiparametric spatial dependence approach," Papers in Regional Science, Wiley Blackwell, vol. 87(4), pages 527-544, November.
    15. Lan Wang, 2009. "Wilcoxon-type generalized Bayesian information criterion," Biometrika, Biometrika Trust, vol. 96(1), pages 163-173.
    16. 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.
    17. Wu, Tracy Z. & Yu, Keming & Yu, Yan, 2010. "Single-index quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1607-1621, August.
    18. Yan Fan & Wolfgang Karl Härdle & Weining Wang & Lixing Zhu, 2018. "Single-Index-Based CoVaR With Very High-Dimensional Covariates," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(2), pages 212-226, April.
    19. 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.
    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. 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.
    2. Fang Lu & Guoliang Tian & Jing Yang, 2024. "GMM estimation and variable selection of partially linear additive spatial autoregressive model," Statistical Papers, Springer, vol. 65(4), pages 2253-2288, June.
    3. 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.
    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. Long Feng & Changliang Zou & Zhaojun Wang & Xianwu Wei & Bin Chen, 2015. "Robust spline-based variable selection in varying coefficient model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(1), pages 85-118, January.
    6. Yangbing Tang & Zhongzhan Zhang & Jiang Du, 2024. "Rank-based instrumental variable estimation for semiparametric varying coefficient spatial autoregressive models," Statistical Papers, Springer, vol. 65(3), pages 1805-1839, May.
    7. 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).
    8. Luo, Guowang & Wu, Mixia & Pang, Zhen, 2022. "Estimation of spatial autoregressive models with covariate measurement errors," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    9. 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.
    10. Mu Yue & Jingxin Xi, 2025. "Sparse Boosting for Additive Spatial Autoregressive Model with High Dimensionality," Mathematics, MDPI, vol. 13(5), pages 1-16, February.
    11. Yazhao Lv & Riquan Zhang & Weihua Zhao & Jicai Liu, 2014. "Quantile regression and variable selection for the single-index model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(7), pages 1565-1577, July.
    12. Rong Jiang & Mengxian Sun, 2022. "Single-index composite quantile regression for ultra-high-dimensional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 443-460, June.
    13. 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.
    14. Mustafa Koroglu & Yiguo Sun, 2016. "Functional-Coefficient Spatial Durbin Models with Nonparametric Spatial Weights: An Application to Economic Growth," Econometrics, MDPI, vol. 4(1), pages 1-16, February.
    15. Kwok, Hon Ho, 2019. "Identification and estimation of linear social interaction models," Journal of Econometrics, Elsevier, vol. 210(2), pages 434-458.
    16. Xuan Liu & Jianbao Chen, 2021. "Variable Selection for the Spatial Autoregressive Model with Autoregressive Disturbances," Mathematics, MDPI, vol. 9(12), pages 1-20, June.
    17. Jianbo Li & Yuan Li & Riquan Zhang, 2017. "B spline variable selection for the single index models," Statistical Papers, Springer, vol. 58(3), pages 691-706, September.
    18. Xiuli Wang & Jingchang Shao & Jingjing Wu & Qiang Zhao, 2023. "Robust variable selection with exponential squared loss for partially linear spatial autoregressive models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(6), pages 949-977, December.
    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. Cheng, Suli & Chen, Jianbao, 2023. "GMM estimation of partially linear additive spatial autoregressive model," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).

    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:kap:netspa:v:24:y:2024:i:2:d:10.1007_s11067-024-09616-4. 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.