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Model Selection for High Dimensional Nonparametric Additive Models via Ridge Estimation

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  • Haofeng Wang

    (Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
    Department of Statistics and Data Science, Southern University of Science and Technology, Shenzhen 518055, China)

  • Hongxia Jin

    (Department of Statistics and Data Science, Southern University of Science and Technology, Shenzhen 518055, China)

  • Xuejun Jiang

    (Department of Statistics and Data Science, Southern University of Science and Technology, Shenzhen 518055, China)

  • Jingzhi Li

    (Department of Mathematics, Southern University of Science and Technology, Shenzhen 518055, China)

Abstract

In ultrahigh dimensional data analysis, to keep computational performance well and good statistical properties still working, nonparametric additive models face increasing challenges. To overcome them, we introduce a methodology of model selection for high dimensional nonparametric additive models. Our approach is to propose a novel group screening procedure via nonparametric smoothing ridge estimation (GRIE) to find the importance of each covariate. It is then combined with the sure screening property of GRIE and the model selection property of extended Bayesian information criteria (EBIC) to select the suitable sub-models in nonparametric additive models. Theoretically, we establish the strong consistency of model selection for the proposed method. Extensive simulations and two real datasets illustrate the outstanding performance of the GRIE-EBIC method.

Suggested Citation

  • Haofeng Wang & Hongxia Jin & Xuejun Jiang & Jingzhi Li, 2022. "Model Selection for High Dimensional Nonparametric Additive Models via Ridge Estimation," Mathematics, MDPI, vol. 10(23), pages 1-22, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4551-:d:990469
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    References listed on IDEAS

    as
    1. Ning Hao & Hao Helen Zhang, 2017. "A Note on High-Dimensional Linear Regression With Interactions," The American Statistician, Taylor & Francis Journals, vol. 71(4), pages 291-297, October.
    2. Jiahua Chen & Zehua Chen, 2008. "Extended Bayesian information criteria for model selection with large model spaces," Biometrika, Biometrika Trust, vol. 95(3), pages 759-771.
    3. Junwei Lu & Mladen Kolar & Han Liu, 2020. "Kernel Meets Sieve: Post-Regularization Confidence Bands for Sparse Additive Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(532), pages 2084-2099, December.
    4. Ming-Yen Cheng & Toshio Honda & Jin-Ting Zhang, 2016. "Forward Variable Selection for Sparse Ultra-High Dimensional Varying Coefficient Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(515), pages 1209-1221, July.
    5. 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.
    6. Ray Bai & Gemma E. Moran & Joseph L. Antonelli & Yong Chen & Mary R. Boland, 2022. "Spike-and-Slab Group Lassos for Grouped Regression and Sparse Generalized Additive Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(537), pages 184-197, January.
    7. Xiangyu Wang & Chenlei Leng, 2016. "High dimensional ordinary least squares projection for screening variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(3), pages 589-611, June.
    8. Fan, Jianqing & Feng, Yang & Song, Rui, 2011. "Nonparametric Independence Screening in Sparse Ultra-High-Dimensional Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 544-557.
    9. Jianqing Fan & Yunbei Ma & Wei Dai, 2014. "Nonparametric Independence Screening in Sparse Ultra-High-Dimensional Varying Coefficient Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1270-1284, September.
    10. Tingyou Zhou & Liping Zhu & Chen Xu & Runze Li, 2020. "Model-Free Forward Screening Via Cumulative Divergence," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(531), pages 1393-1405, July.
    11. 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.
    12. 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.
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