Adaptive group Lasso for high-dimensional generalized linear models

Variable selection in a grouped manner is an attractive method since it respects the grouping structure in the data. In this paper, we study the adaptive group Lasso in the frame of high-dimensional generalized linear models. Both the number of groups diverging with the sample size and the number of groups exceeding the sample size are considered. The selection consistency and asymptotic normality of the adaptive group Lasso are established under appropriate conditions. Simulation studies confirm superior performances of the adaptive group Lasso.