组合惩罚似然估计下发散参数变量选择

在Wang等给出的组合惩罚函数的基础之上,将SCAD惩罚部分推广到一般的非凸惩罚的形式,利用岭回归在解释变量相关度较高情形下的良好表现,提出一种推广了的组合惩罚.在参数个数发散的情形之下,利用贝叶斯信息准则(BIC)来选择调整参数,能同时完成变量选择和参数估计.而且还可以证明在合适的条件之下,这种估计具有Oracle性质.模拟研究的结果证明了所提出的方法在预测变量具有强相关性之下的优势.

Variable selection of diverging number of parameters under combined penalized likelihood estimations

Based on the combined penalized function of Wang, et al. , a generalized combined penalization is proposed, in which the SCAD penalization is extended to the general nonconcave penalization, and the ridge regression performs well when the predictors are highly correlated. With a diverging number of parameters, the Bayesian information criterion (BIC) is used to choose tuning parameters. Then, it is shown that the variable selection and parameter estimation can be fulfilled simultaneously. Furthermore, under the appropriate conditions, the estimator possesses the Oracle property. The simulation studies demonstrate the practical superiority of the proposed method when high correlation exists among predictors.