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Estimation of partially linear single-index spatial autoregressive model

Author

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  • Suli Cheng

    (Fujian Normal University)

  • Jianbao Chen

    (Fujian Normal University)

Abstract

In this paper, we first present partially linear single-index spatial autoregressive model and propose its profile maximum likelihood estimators (PMLE). Subsequently, consistency and asymptotic normality of the estimators for parameters and unknown link function are derived under some regular conditions. Thirdly, Monte Carlo simulations are used to investigate the performances of these estimators in finite sample cases. Finally, the proposed method is illustrated with the real data set of Boston Housing Price.

Suggested Citation

  • Suli Cheng & Jianbao Chen, 2021. "Estimation of partially linear single-index spatial autoregressive model," Statistical Papers, Springer, vol. 62(1), pages 495-531, February.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:1:d:10.1007_s00362-019-01105-y
    DOI: 10.1007/s00362-019-01105-y
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    References listed on IDEAS

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    1. Yu Y. & Ruppert D., 2002. "Penalized Spline Estimation for Partially Linear Single-Index Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1042-1054, December.
    2. 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.
    3. Su, Liangjun, 2012. "Semiparametric GMM estimation of spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 167(2), pages 543-560.
    4. Pang, Zhen & Xue, Liugen, 2012. "Estimation for the single-index models with random effects," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1837-1853.
    5. Case, Anne C, 1991. "Spatial Patterns in Household Demand," Econometrica, Econometric Society, vol. 59(4), pages 953-965, July.
    6. 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.
    7. Xia, Yingcun & Härdle, Wolfgang, 2006. "Semi-parametric estimation of partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1162-1184, May.
    8. 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.
    9. 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.
    10. Lee, Jiyon, 2015. "A semiparametric single index model with heterogeneous impacts on an unobserved variable," Journal of Econometrics, Elsevier, vol. 184(1), pages 13-36.
    11. Yazhao Lv & Riquan Zhang & Weihua Zhao & Jicai Liu, 2015. "Quantile regression and variable selection of partial linear single-index model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(2), pages 375-409, April.
    12. Tianyong Zhang & Demei Yuan & Jiali Ma & Xuemei Hu, 2017. "Assessing white noise assumption with semi-parametric additive partial linear models," Statistical Papers, Springer, vol. 58(2), pages 417-431, June.
    13. 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.
    14. 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.
    15. Sun, Yan, 2017. "Estimation of single-index model with spatial interaction," Regional Science and Urban Economics, Elsevier, vol. 62(C), pages 36-45.
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    Cited by:

    1. Bogui Li & Jianbao Chen & Shuangshuang Li, 2023. "Estimation of Fixed Effects Partially Linear Varying Coefficient Panel Data Regression Model with Nonseparable Space-Time Filters," Mathematics, MDPI, vol. 11(6), pages 1-24, March.
    2. 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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