这份报纸采用惩罚大量的最少的广场方法同时选择变量并且估计为高度维的 covariate 的系数调整了线性回归模型。弄歪的变量被假定与被看得见的 covariate 的一个未知函数的值决定的一个趋于增加的因素被污染。作者证明在一些适当条件下面,惩罚大量的最少的广场评估者有所谓的神谕性质。另外,作者也建议一个 BIC 标准选择调节参数,并且证明那个 BIC 标准能一致地识别真正的模型因为 covariate 调整了线性回归模型。模拟研究和一个真实数据被用来说明建议评价算法的效率。
This paper employs the SCAD-penalized least squares method to simultaneously select variables and estimate the coefficients for high-dimensional covariate adjusted linear regression models. The distorted variables are assumed to be contaminated with a multiplicative factor that is determined by the value of an unknown function of an observable covariate. The authors show that under some appropriate conditions, the SCAD-penalized least squares estimator has the so called "oracle property". In addition, the authors also suggest a BIC criterion to select the tuning parameter, and show that BIC criterion is able to identify the true model consistently for the covariate adjusted linear regression models. Simulation studies and a real data are used to illustrate the efficiency of the proposed estimation algorithm.