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Sparse Boosting for Additive Spatial Autoregressive Model with High Dimensionality

Author

Listed:
  • Mu Yue

    (School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 639798, Singapore)

  • Jingxin Xi

    (School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 639798, Singapore
    School of Ecology & Environment, Renmin University of China, Beijing 100872, China)

Abstract

Variable selection methods have been a focus in the context of econometrics and statistics literature. In this paper, we consider additive spatial autoregressive model with high-dimensional covariates. Instead of adopting the traditional regularization approaches, we offer a novel multi-step sparse boosting algorithm to conduct model-based prediction and variable selection. One main advantage of this new method is that we do not need to perform the time-consuming selection of tuning parameters. Extensive numerical examples illustrate the advantage of the proposed methodology. An application of Boston housing price data is further provided to demonstrate the proposed methodology.

Suggested Citation

  • Mu Yue & Jingxin Xi, 2025. "Sparse Boosting for Additive Spatial Autoregressive Model with High Dimensionality," Mathematics, MDPI, vol. 13(5), pages 1-16, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:5:p:757-:d:1599548
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    References listed on IDEAS

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    1. 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.
    2. Su, Liangjun, 2012. "Semiparametric GMM estimation of spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 167(2), pages 543-560.
    3. Gilley, Otis W. & Pace, R. Kelley, 1996. "On the Harrison and Rubinfeld Data," Journal of Environmental Economics and Management, Elsevier, vol. 31(3), pages 403-405, November.
    4. Zixin Yang & Xiaojun Song & Jihai Yu, 2024. "Model Checking in Partially Linear Spatial Autoregressive Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 42(4), pages 1210-1222, October.
    5. 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.
    6. Yousuf, Kashif & Ng, Serena, 2021. "Boosting high dimensional predictive regressions with time varying parameters," Journal of Econometrics, Elsevier, vol. 224(1), pages 60-87.
    7. Miaojie Xia & Yuqi Zhang & Ruiqin Tian & Antonio Di Crescenzo, 2023. "Variable Selection of High-Dimensional Spatial Autoregressive Panel Models with Fixed Effects," Journal of Mathematics, Hindawi, vol. 2023, pages 1-16, May.
    8. 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.
    9. 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.
    10. 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.
    11. Yue, Mu & Li, Jialiang & Cheng, Ming-Yen, 2019. "Two-step sparse boosting for high-dimensional longitudinal data with varying coefficients," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 222-234.
    12. Zhenlin Yang & Liangjun Su, 2007. "Instrumental Variable Quantile Estimation of Spatial Autoregressive Models," Working Papers 05-2007, Singapore Management University, School of Economics.
    13. Li, Hongfei & Calder, Catherine A. & Cressie, Noel, 2012. "One-step estimation of spatial dependence parameters: Properties and extensions of the APLE statistic," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 68-84.
    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. Jianqing Fan & Jinchi Lv, 2008. "Sure independence screening for ultrahigh dimensional feature space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 849-911, November.
    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. Liu, Xiaodong & Lee, Lung-fei & Bollinger, Christopher R., 2010. "An efficient GMM estimator of spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 159(2), pages 303-319, December.
    18. Hongjie Wei & Yan Sun & Meidi Hu, 2018. "Model Selection in Spatial Autoregressive Models with Varying Coefficients," Frontiers of Economics in China-Selected Publications from Chinese Universities, Higher Education Press, vol. 13(4), pages 559-576, December.
    19. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
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