测量误差模型的自适应LASSO变量选择方法研究

Adaptive LASSO for measurement error models

本文研究测量误差模型的自适应LASSO(least absolute shrinkage and selection operator)变量选择和系数估计问题.首先分别给出协变量有测量误差时的线性模型和部分线性模型自适应LASSO参数估计量,在一些正则条件下研究估计量的渐近性质,并且证明选择合适的调整参数,自适应LASSO参数估计量具有oracle性质.其次讨论估计的实现算法及惩罚参数和光滑参数的选择问题.最后通过模拟和一个实际数据分析研究了自适应LASSO变量选择方法的表现,结果表明,变量选择和参数估计效果良好.

This paper focuses on variable selection and parameter estimation for measurement error models via adaptive LASSO method.Firstly,the adaptive LASSO estimator for linear models and partially linear models are proposed when the covariates are measured with error.Under some regular conditions the asymptotic properties of the estimators are investigated,it is proved that the adaptive lasso estimator has the oracle properties with proper choices of tuning parameter.Moreover,the algorithms and choices of penalty parameter and bandwidth are discussed.Finally,a Monte Carlo simulation study and a real data analysis are conducted to assess the finite sample performance of the proposed variable selection procedure.The results show that the adaptive LASSO estimator behaves well.