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Adaptive Lasso for generalized linear models with a diverging number of parameters

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  • Yan Cui
  • Xia Chen
  • Li Yan

Abstract

In this paper, we study the asymptotic properties of the adaptive Lasso estimators in high-dimensional generalized linear models. The consistency of the adaptive Lasso estimator is obtained. We show that, if a reasonable initial estimator is available, under appropriate conditions, the adaptive Lasso correctly selects covariates with non zero coefficients with probability converging to one, and that the estimators of non zero coefficients have the same asymptotic distribution they would have if the zero coefficients were known in advance. Thus, the adaptive Lasso has an Oracle property. The results are examined by some simulations and a real example.

Suggested Citation

  • Yan Cui & Xia Chen & Li Yan, 2017. "Adaptive Lasso for generalized linear models with a diverging number of parameters," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(23), pages 11826-11842, December.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:23:p:11826-11842
    DOI: 10.1080/03610926.2017.1285926
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