The Asymptotic Properties of Scad Penalized Generalized Linear Models with Adaptive Designs

This paper discusses the asymptotic properties of the SCAD(smoothing clipped absolute deviation) penalized quasi-likelihood estimator for generalized linear models with adaptive designs,which extend the related results for independent observations to dependent observations. Under certain conditions, the authors proved that the SCAD penalized method correctly selects covariates with nonzero coefficients with probability converging to one, and the penalized quasi-likelihood estimators of non-zero coefficients have the same asymptotic distribution they would have if the zero coefficients were known in advance. That is, the SCAD estimator has consistency and oracle properties. At last, the results are illustrated by some simulations.