纵向数据下部分线性单指标模型的变量选择

Variable Selection for Partial Linear Single Index Model under Longitudinal Data

研究各种复杂数据之间的关系以及研究各种模型中各个有效协变量的选择方法是统计学研究领域的一项重要的工作。针对纵向数据下的部分线性单指标模型,采用对其线性部分参数与单指标部分的参数的估计与变量选择同时进行SCAD、LASSO、ALASSO惩罚的方法。并且在一定的条件下,证明了一些惩罚估计量有Oracle性质,其结果是参数估计的渐进均值、渐进协方差与参数真实值的渐进均值、渐进协方差相同。还利用随机模拟方法,研究了估计的大样本性质,说明所提出的方法对于参数的变量选择是可行的。

It is an important work in the field of statistical research to study the relationship between various complex data and the selection methods of effective covariates in various models.Here according to the partial linear single index model under longitudinal data,the method of carrying out SCAD,LASSO and ALASSO penalty at the same time by parameter estimation and variable selection for the linear part parameter and the single index part was adopted.And under certain conditions,we proved that some penalty estimators had Oracle property,which was the asymptotic mean and asymptotic covariance of the parameter estimate were the same as the asymptotic mean and asymptotic covariance of the real We also used stochastic simulation methods to study the large sample properties of estimators.It showed that our proposed method was feasible for variable selection of parameters.