IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i10p1680-d422575.html
   My bibliography  Save this article

Estimation in Partial Functional Linear Spatial Autoregressive Model

Author

Listed:
  • Yuping Hu

    (School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China)

  • Siyu Wu

    (School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China)

  • Sanying Feng

    (School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
    Henan Key Laboratory of Financial Engineering, Zhengzhou University, Zhengzhou 450001, China)

  • Junliang Jin

    (School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China)

Abstract

Functional regression allows for a scalar response to be dependent on a functional predictor; however, not much work has been done when response variables are dependence spatial variables. In this paper, we introduce a new partial functional linear spatial autoregressive model which explores the relationship between a scalar dependence spatial response variable and explanatory variables containing both multiple real-valued scalar variables and a function-valued random variable. By means of functional principal components analysis and the instrumental variable estimation method, we obtain the estimators of the parametric component and slope function of the model. Under some regularity conditions, we establish the asymptotic normality for the parametric component and the convergence rate for slope function. At last, we illustrate the finite sample performance of our proposed methods with some simulation studies.

Suggested Citation

  • Yuping Hu & Siyu Wu & Sanying Feng & Junliang Jin, 2020. "Estimation in Partial Functional Linear Spatial Autoregressive Model," Mathematics, MDPI, vol. 8(10), pages 1-12, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1680-:d:422575
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/10/1680/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/10/1680/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Case, Anne C, 1991. "Spatial Patterns in Household Demand," Econometrica, Econometric Society, vol. 59(4), pages 953-965, July.
    2. Dehan Kong & Kaijie Xue & Fang Yao & Hao H. Zhang, 2016. "Partially functional linear regression in high dimensions," Biometrika, Biometrika Trust, vol. 103(1), pages 147-159.
    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. Ping Yu & Zhongzhan Zhang & Jiang Du, 2016. "A test of linearity in partial functional linear regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(8), pages 953-969, November.
    5. Ying Lu & Jiang Du & Zhimeng Sun, 2014. "Functional partially linear quantile regression model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(2), pages 317-332, February.
    6. 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.
    7. Dauxois, J. & Pousse, A. & Romain, Y., 1982. "Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference," Journal of Multivariate Analysis, Elsevier, vol. 12(1), pages 136-154, March.
    8. 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.
    9. Lian, Heng & Li, Gaorong, 2014. "Series expansion for functional sufficient dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 150-165.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Gurami Tsitsiashvili & Marina Osipova & Yury Kharchenko, 2022. "Estimating the Coefficients of a System of Ordinary Differential Equations Based on Inaccurate Observations," Mathematics, MDPI, vol. 10(3), pages 1-9, February.

    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. Gupta, Abhimanyu, 2019. "Estimation Of Spatial Autoregressions With Stochastic Weight Matrices," Econometric Theory, Cambridge University Press, vol. 35(2), pages 417-463, April.
    2. repec:esx:essedp:772 is not listed on IDEAS
    3. Gupta, A, 2015. "Nonparametric specification testing via the trinity of tests," Economics Discussion Papers 15619, University of Essex, Department of Economics.
    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. 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.
    6. Abhimanyu Gupta & Xi Qu, 2021. "Consistent specification testing under spatial dependence," Papers 2101.10255, arXiv.org, revised Aug 2022.
    7. Gupta, Abhimanyu, 2018. "Nonparametric specification testing via the trinity of tests," Journal of Econometrics, Elsevier, vol. 203(1), pages 169-185.
    8. repec:esx:essedp:774 is not listed on IDEAS
    9. Gupta, Abhimanyu & Robinson, Peter M., 2015. "Inference on higher-order spatial autoregressive models with increasingly many parameters," Journal of Econometrics, Elsevier, vol. 186(1), pages 19-31.
    10. Théophile Azomahou, 2008. "Minimum distance estimation of the spatial panel autoregressive model," Cliometrica, Journal of Historical Economics and Econometric History, Association Française de Cliométrie (AFC), vol. 2(1), pages 49-83, April.
    11. 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.
    12. 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.
    13. Liu, Shew Fan & Yang, Zhenlin, 2015. "Modified QML estimation of spatial autoregressive models with unknown heteroskedasticity and nonnormality," Regional Science and Urban Economics, Elsevier, vol. 52(C), pages 50-70.
    14. Lee, Lung-fei & Yu, Jihai, 2010. "Some recent developments in spatial panel data models," Regional Science and Urban Economics, Elsevier, vol. 40(5), pages 255-271, September.
    15. 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.
    16. Luo, Guowang & Wu, Mixia & Pang, Zhen, 2022. "Estimation of spatial autoregressive models with covariate measurement errors," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    17. Yu, Dengdeng & Zhang, Li & Mizera, Ivan & Jiang, Bei & Kong, Linglong, 2019. "Sparse wavelet estimation in quantile regression with multiple functional predictors," Computational Statistics & Data Analysis, Elsevier, vol. 136(C), pages 12-29.
    18. Kyriacou, Maria & Phillips, Peter C.B. & Rossi, Francesca, 2023. "Continuously Updated Indirect Inference In Heteroskedastic Spatial Models," Econometric Theory, Cambridge University Press, vol. 39(1), pages 107-145, February.
    19. Kapoor, Mudit & Kelejian, Harry H. & Prucha, Ingmar R., 2007. "Panel data models with spatially correlated error components," Journal of Econometrics, Elsevier, vol. 140(1), pages 97-130, September.
    20. Xuan Liang & Jiti Gao & Xiaodong Gong, 2022. "Semiparametric Spatial Autoregressive Panel Data Model with Fixed Effects and Time-Varying Coefficients," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(4), pages 1784-1802, October.
    21. 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.
    22. 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.

    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:gam:jmathe:v:8:y:2020:i:10:p:1680-:d:422575. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.