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Variable selection for spatial autoregressive models with a diverging number of parameters

Author

Listed:
  • Tianfa Xie

    (Beijing University of Technology)

  • Ruiyuan Cao

    (Beijing University of Technology)

  • Jiang Du

    (Beijing University of Technology)

Abstract

Variable selection has played a fundamental role in regression analysis. Spatial autoregressive model is a useful tool in econometrics and statistics in which context variable selection is necessary but not adequately investigated. In this paper, we consider conducting variable selection in spatial autoregressive models with a diverging number of parameters. Smoothly clipped absolute deviation penalty is considered to obtain the estimators. Moreover the dimension of the covariates are allowed to vary with sample size. In order to attenuate the bias caused by endogeneity, instrumental variable is adopted in the estimation procedure. The proposed method can do parametric estimation and variable selection simultaneously. Under mild conditions, we establish the asymptotic and oracle property of the proposed estimators. Finally, the performance of the proposed estimation procedure is examined via Monte Carlo simulation studies and a data set from a Boston housing price is analyzed as an illustrative example.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:3:d:10.1007_s00362-018-0984-2
    DOI: 10.1007/s00362-018-0984-2
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    Cited by:

    1. He Jiang, 2023. "Robust forecasting in spatial autoregressive model with total variation regularization," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 42(2), pages 195-211, March.
    2. Yunquan Song & Minmin Zhan & Yue Zhang & Yongxin Liu, 2024. "Huber Loss Meets Spatial Autoregressive Model: A Robust Variable Selection Method with Prior Information," Networks and Spatial Economics, Springer, vol. 24(1), pages 291-311, March.
    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. Ruiqin Tian & Miaojie Xia & Dengke Xu, 2024. "Profile quasi-maximum likelihood estimation for semiparametric varying-coefficient spatial autoregressive panel models with fixed effects," Statistical Papers, Springer, vol. 65(8), pages 5109-5143, October.
    5. 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.
    6. 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.
    7. Yuanying Zhao & Dengke Xu, 2023. "A Bayesian Variable Selection Method for Spatial Autoregressive Quantile Models," Mathematics, MDPI, vol. 11(4), pages 1-19, February.
    8. 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).
    9. Xuan Liu & Jianbao Chen, 2021. "Variable Selection for the Spatial Autoregressive Model with Autoregressive Disturbances," Mathematics, MDPI, vol. 9(12), pages 1-20, June.

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