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 non-zero 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.

本文讨论了具有自适应设计的广义线性模型的SCAD（平滑修剪绝对偏差）惩罚拟似然估计的渐近性质，并将独立观测的相关结果扩展到相关观测。在某些条件下，作者证明了SCAD罚分法正确选择了概率为1的非零系数协变量，并且非零系数的罚拟似然估计值与零系数时的渐近分布相同。事先知道。也就是说，SCAD估计器具有一致性和oracle属性。最后，通过一些仿真说明了结果。