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Bayesian Adaptive Lasso for the Partial Functional Linear Spatial Autoregressive Model

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  • Dengke Xu
  • Ruiqin Tian
  • Ying Lu

Abstract

This study introduces a partial functional linear spatial autoregressive model which can explore the relationship between a scalar spatially dependent response variable and predictive variables containing both multiple scalar covariates and a functional covariate. With approximating to the functional coefficient by Karhunen–Loève representation, we propose a Bayesian adaptive Lasso method to simultaneously estimate unknown parameters and select important covariates in the model, which can be performed by combining the Gibbs sampler and the Metropolis–Hastings algorithm. Some simulation studies are conducted and the results show that the proposed Bayesian method behaves well.

Suggested Citation

  • Dengke Xu & Ruiqin Tian & Ying Lu, 2022. "Bayesian Adaptive Lasso for the Partial Functional Linear Spatial Autoregressive Model," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:1616068
    DOI: 10.1155/2022/1616068
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    References listed on IDEAS

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    1. 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.
    2. Xu, Dengke & Zhang, Zhongzhan, 2013. "A semiparametric Bayesian approach to joint mean and variance models," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1624-1631.
    3. 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.
    4. 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.
    5. Ping Yu & Jiang Du & Zhongzhan Zhang, 2020. "Single-index partially functional linear regression model," Statistical Papers, Springer, vol. 61(3), pages 1107-1123, June.
    6. Zhou, Jianjun & Peng, Qingyan, 2020. "Estimation for functional partial linear models with missing responses," Statistics & Probability Letters, Elsevier, vol. 156(C).
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