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Estimation of single-index model with spatial interaction

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  • Sun, Yan

Abstract

This article is concerned with the single-index model in spatial dependence data, 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. This setup avoids the so-called curse of dimensionality while still capturing important nonlinear features in high dimensional data. It also provides a convenient framework in which to model interactions between the regressors. We propose a two stage estimation strategy where the nonparametric component is established by a local linear approach and the estimation of the parametric part by GMM method, which can be seen as a direct nonlinear least squares method. We derive the asymptotic distributions of the unknowns in our model, and the procedures for constructing simultaneous confidence bands of the nonparametric function are also established. In addition, a simulation study is performed.

Suggested Citation

  • Sun, Yan, 2017. "Estimation of single-index model with spatial interaction," Regional Science and Urban Economics, Elsevier, vol. 62(C), pages 36-45.
    • Handle: RePEc:eee:regeco:v:62:y:2017:i:c:p:36-45
    DOI: 10.1016/j.regsciurbeco.2016.11.004
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    References listed on IDEAS

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    1. Su, Liangjun, 2012. "Semiparametric GMM estimation of spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 167(2), pages 543-560.
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    7. Basile, Roberto & Durbán, María & Mínguez, Román & María Montero, Jose & Mur, Jesús, 2014. "Modeling regional economic dynamics: Spatial dependence, spatial heterogeneity and nonlinearities," Journal of Economic Dynamics and Control, Elsevier, vol. 48(C), pages 229-245.
    8. 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.
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    10. 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.
    11. 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.
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    Cited by:

    1. Jianbao Chen & Suli Cheng, 2021. "GMM Estimation of a Partially Linear Additive Spatial Error Model," Mathematics, MDPI, vol. 9(6), pages 1-28, March.
    2. Suli Cheng & Jianbao Chen, 2021. "Estimation of partially linear single-index spatial autoregressive model," Statistical Papers, Springer, vol. 62(1), pages 495-531, February.
    3. 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.
    4. 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.

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