A general adaptive ridge regression method for generalized linear models: an iterative re-weighting approach

This article is concerned with the problem of variable selection and estimation for high dimensional generalized linear models. In this article, we introduce a general iteratively reweighted adaptive ridge regression method (GAR). We show that the GAR estimator possesses oracle property and grouping effect. A data-driven parameter γ is introduced in the GAR method to adapt the different cases of the true model. Then, such an adaptive parameter γ is adequately taken into consideration to establish a γ-dependent sufficient condition to guarantee the oracle property and the grouping effect. Furthermore, to apply the GAR method more efficiently, a coordinate-wise Newton algorithm is employed to successfully avoid the inverse matrix operation and the numerical instability caused by iteration. Extensive numerical simulation results show that the GAR method outperforms the commonly used methods, and the GAR method is tested on the gastric cancer dataset for further illustration.