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Partially linear structure identification in generalized additive models with NP-dimensionality

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  • Lian, Heng
  • Du, Pang
  • Li, YuanZhang
  • Liang, Hua

Abstract

Separation of the linear and nonlinear components in additive models based on penalized likelihood has received attention recently. However, it remains unknown whether consistent separation is possible in generalized additive models, and how high dimensionality is allowed. In this article, we study the doubly SCAD-penalized approach for partial linear structure identification problems of non-polynomial (NP) dimensionality and demonstrate its oracle property. In particular, if the number of nonzero components is fixed, the dimensionality of the total number of components can be of order exp{nd/(2d+1)} where d is the smoothness of the component functions. Under such dimensionality assumptions, we show that with probability approaching one, the proposed procedure can correctly identify the zero, linear, and nonlinear components in the model. We further establish the convergence rate of the estimator for the nonlinear component and the asymptotic normality of the estimator for the linear component. Performance of the proposed method is evaluated by simulation studies. The methods are demonstrated by analyzing a gene data set.

Suggested Citation

  • Lian, Heng & Du, Pang & Li, YuanZhang & Liang, Hua, 2014. "Partially linear structure identification in generalized additive models with NP-dimensionality," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 197-208.
    • Handle: RePEc:eee:csdana:v:80:y:2014:i:c:p:197-208
    DOI: 10.1016/j.csda.2014.06.021
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Lin X. & Carroll R. J., 2001. "Semiparametric Regression for Clustered Data Using Generalized Estimating Equations," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1045-1056, September.
    4. 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.
    5. Laura J. van 't Veer & Hongyue Dai & Marc J. van de Vijver & Yudong D. He & Augustinus A. M. Hart & Mao Mao & Hans L. Peterse & Karin van der Kooy & Matthew J. Marton & Anke T. Witteveen & George J. S, 2002. "Gene expression profiling predicts clinical outcome of breast cancer," Nature, Nature, vol. 415(6871), pages 530-536, January.
    6. Zhang, Hao Helen & Cheng, Guang & Liu, Yufeng, 2011. "Linear or Nonlinear? Automatic Structure Discovery for Partially Linear Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1099-1112.
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    Cited by:

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    2. Giordano, Francesco & Milito, Sara & Parrella, Maria Lucia, 2023. "Linear and nonlinear effects explaining the risk of Covid-19 infection: an empirical analysis on real data from the USA," Socio-Economic Planning Sciences, Elsevier, vol. 90(C).

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