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Variable selection for partially linear models via Bayesian subset modeling with diffusing prior

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  • Wang, Jia
  • Cai, Xizhen
  • Li, Runze

Abstract

Most existing methods of variable selection in partially linear models (PLM) with ultrahigh dimensional covariates are based on partial residuals, which involve a two-step estimation procedure. While the estimation error produced in the first step may have an impact on the second step, multicollinearity among predictors adds additional challenges in the model selection procedure. In this paper, we propose a new Bayesian variable selection approach for PLM. This new proposal addresses those two issues simultaneously as (1) it is a one-step method which selects variables in PLM, even when the dimension of covariates increases at an exponential rate with the sample size, and (2) the method retains model selection consistency, and outperforms existing ones in the setting of highly correlated predictors. Distinguished from existing ones, our proposed procedure employs the difference-based method to reduce the impact from the estimation of the nonparametric component, and incorporates Bayesian subset modeling with diffusing prior (BSM-DP) to shrink the corresponding estimator in the linear component. The estimation is implemented by Gibbs sampling, and we prove that the posterior probability of the true model being selected converges to one asymptotically. Simulation studies support the theory and the efficiency of our methods as compared to other existing ones, followed by an application in a study of supermarket data.

Suggested Citation

  • Wang, Jia & Cai, Xizhen & Li, Runze, 2021. "Variable selection for partially linear models via Bayesian subset modeling with diffusing prior," Journal of Multivariate Analysis, Elsevier, vol. 183(C).
    • Handle: RePEc:eee:jmvana:v:183:y:2021:i:c:s0047259x21000117
    DOI: 10.1016/j.jmva.2021.104733
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    References listed on IDEAS

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    1. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    2. Valen E. Johnson & David Rossell, 2012. "Bayesian Model Selection in High-Dimensional Settings," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 649-660, June.
    3. Faming Liang & Qifan Song & Kai Yu, 2013. "Bayesian Subset Modeling for High-Dimensional Generalized Linear Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 589-606, June.
    4. Zhao Chen & Jianqing Fan & Runze Li, 2018. "Error Variance Estimation in Ultrahigh-Dimensional Additive Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(521), pages 315-327, January.
    5. Liu, Jingyuan & Lou, Lejia & Li, Runze, 2018. "Variable selection for partially linear models via partial correlation," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 418-434.
    6. P. Bühlmann & M. Kalisch & M. H. Maathuis, 2010. "Variable selection in high-dimensional linear models: partially faithful distributions and the pc -simple algorithm," Biometrika, Biometrika Trust, vol. 97(2), pages 261-278.
    7. Liang, Hua & Li, Runze, 2009. "Variable Selection for Partially Linear Models With Measurement Errors," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 234-248.
    8. Naveen N. Narisetty & Juan Shen & Xuming He, 2019. "Skinny Gibbs: A Consistent and Scalable Gibbs Sampler for Model Selection," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(527), pages 1205-1217, July.
    9. Yuan, Ming & Lin, Yi, 2005. "Efficient Empirical Bayes Variable Selection and Estimation in Linear Models," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1215-1225, December.
    10. Yatchew, A., 1997. "An elementary estimator of the partial linear model," Economics Letters, Elsevier, vol. 57(2), pages 135-143, December.
    11. 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.
    12. Ming Yuan & Yi Lin, 2007. "On the non‐negative garrotte estimator," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(2), pages 143-161, April.
    13. 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.
    14. Rice, John, 1986. "Convergence rates for partially splined models," Statistics & Probability Letters, Elsevier, vol. 4(4), pages 203-208, June.
    15. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    16. Wang, Hansheng, 2009. "Forward Regression for Ultra-High Dimensional Variable Screening," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1512-1524.
    17. Gong, Siliang & Zhang, Kai & Liu, Yufeng, 2018. "Efficient test-based variable selection for high-dimensional linear models," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 17-31.
    18. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    19. Ishwaran, Hemant & Sunil Rao, J., 2011. "Consistency of spike and slab regression," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1920-1928.
    Full references (including those not matched with items on IDEAS)

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