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

作者：Cui, Yan; Chen, Xia^*; Yan, Li

来源：Communications in Statistics - Theory and Methods, 2017, 46(23): 11826-11842.

DOI：10.1080/03610926.2017.1285926

• Adaptive lasso
• generalized linear models
• high-dimensional data
• oracle property
• variable selection

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.

• 出版日期2017
• 单位陕西师范大学