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Sequential profile Lasso for ultra-high-dimensional partially linear models

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  • Yujie Li
  • Gaorong Li
  • Tiejun Tong

Abstract

In this paper, we study ultra-high-dimensional partially linear models when the dimension of the linear predictors grows exponentially with the sample size. For the variable screening, we propose a sequential profile Lasso method (SPLasso) and show that it possesses the screening property. SPLasso can also detect all relevant predictors with probability tending to one, no matter whether the ultra-high models involve both parametric and nonparametric parts. To select the best subset among the models generated by SPLasso, we propose an extended Bayesian information criterion (EBIC) for choosing the final model. We also conduct simulation studies and apply a real data example to assess the performance of the proposed method and compare with the existing method.

Suggested Citation

  • Yujie Li & Gaorong Li & Tiejun Tong, 2017. "Sequential profile Lasso for ultra-high-dimensional partially linear models," Statistical Theory and Related Fields, Taylor & Francis Journals, vol. 1(2), pages 234-245, July.
    • Handle: RePEc:taf:tstfxx:v:1:y:2017:i:2:p:234-245
    DOI: 10.1080/24754269.2017.1396432
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    Cited by:

    1. Zhang, Shen & Zhao, Peixin & Li, Gaorong & Xu, Wangli, 2019. "Nonparametric independence screening for ultra-high dimensional generalized varying coefficient models with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 37-52.
    2. Zheng, Zemin & Li, Yang & Yu, Chongxiu & Li, Gaorong, 2018. "Balanced estimation for high-dimensional measurement error models," Computational Statistics & Data Analysis, Elsevier, vol. 126(C), pages 78-91.

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