GENERALIZED ADDITIVE PARTIAL LINEAR MODELS WITH HIGH-DIMENSIONAL COVARIATES
研究了高维协变量下广义可加部分线性模型的变量选择与估计问题，提出双重惩罚方法结合自适应LASSO来识别非零成分，并证明了估计量的相合性和渐近正态性。
This paper studies generalized additive partial linear models with high-dimensional covariates. We are interested in which components (including parametric and nonparametric components) are nonzero. The additive nonparametric functions are approximated by polynomial splines. We propose a doubly penalized procedure to obtain an initial estimate and then use the adaptive least absolute shrinkage and selection operator to identify nonzero components and to obtain the final selection and estimation results. We establish selection and estimation consistency of the estimator in addition to asymptotic normality for the estimator of the parametric components by employing a penalized quasi-likelihood. Thus our estimator is shown to have an asymptotic oracle property. Monte Carlo simulations show that the proposed procedure works well with moderate sample sizes.