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Bridge estimation for generalized linear models with a diverging number of parameters

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  • Wang, Mingqiu
  • Song, Lixin
  • Wang, Xiaoguang

Abstract

Variable selection is fundamental to high dimensional generalized linear models. A number of variable selection approaches have been proposed in the literature. This paper considers the problem of variable selection and estimation in generalized linear models via a bridge penalty in the situation where the number of parameters diverges with the sample size. Under reasonable conditions the consistency of the bridge estimator can be achieved. Furthermore, it can select the nonzero coefficients with a probability converging to 1 and the estimators of nonzero coefficients have the asymptotic normality, namely the oracle property. Our simulations indicate that the bridge penalty is an effective consistent model selection technique and is comparable to the smoothly clipped absolute deviation procedure. A real example analysis is presented.

Suggested Citation

  • Wang, Mingqiu & Song, Lixin & Wang, Xiaoguang, 2010. "Bridge estimation for generalized linear models with a diverging number of parameters," Statistics & Probability Letters, Elsevier, vol. 80(21-22), pages 1584-1596, November.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:21-22:p:1584-1596
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
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    Cited by:

    1. Guo-Liang Tian & Mingqiu Wang & Lixin Song, 2014. "Variable selection in the high-dimensional continuous generalized linear model with current status data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(3), pages 467-483, March.

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