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SCAD-penalised generalised additive models with non-polynomial dimensionality

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  • Gaorong Li
  • Liugen Xue
  • Heng Lian

Abstract

In this article, we study the (group) smoothly clipped absolute deviation (SCAD) estimator in the estimation of generalised additive models. The SCAD penalty, proposed by Fan and Li [(2001) ‘Variable Selection via Nonconcave Penalised Likelihood and Its Oracle Properties’, Journal of the American Statistical Association 96(456), 1348–1360], has many desirable properties including continuity, sparsity and unbiasedness. For high-dimensional parametric models, it has only recently been shown that the SCAD estimator can deal with problems with dimensions much larger than the sample size. Here, we show that the SCAD estimator can be successfully applied to generalised additive models with non-polynomial dimensionality and our study represents the first such result for the SCAD estimator in nonparametric problems, as far as we know. In particular, under suitable assumptions, we theoretically show that the dimension of the problem can be close to expnd/(2d+1), where n is the sample size and d is the smoothness parameter of the component functions. Some Monte Carlo studies and a real data application are also presented.

Suggested Citation

  • Gaorong Li & Liugen Xue & Heng Lian, 2012. "SCAD-penalised generalised additive models with non-polynomial dimensionality," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(3), pages 681-697.
    • Handle: RePEc:taf:gnstxx:v:24:y:2012:i:3:p:681-697
    DOI: 10.1080/10485252.2012.698740
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    References listed on IDEAS

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    Cited by:

    1. Xia Zheng & Yaohua Rong & Ling Liu & Weihu Cheng, 2021. "A More Accurate Estimation of Semiparametric Logistic Regression," Mathematics, MDPI, vol. 9(19), pages 1-12, September.

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