Semiparametric efficient estimation in high‐dimensional partial linear regression models
提出一种新的半参数有效估计方法，用于高维部分线性回归模型，在未知误差分布下克服传统最小二乘的效率损失，实现稀疏估计和半参数效率。
Abstract We introduce a novel semiparametric efficient estimation procedure for high‐dimensional partial linear regression models to overcome the challenge of efficiency loss of the traditional least‐squares based estimation procedure under unknown error distributions, while enjoying several appealing theoretical properties. The new estimation procedure provides a sparse estimator for the parametric component and achieves the semiparametric efficiency as the oracle maximum likelihood estimator as if the error distribution was known. By employing the penalized estimation and the semiparametric efficiency theory for ultra‐high‐dimensional partial linear model, the procedure enjoys the oracle variable selection property and offers efficiency gain for non‐Gaussian random errors, while maintaining the same efficiency as the least squares‐based estimator for Gaussian random errors. Extensive simulation studies and an empirical application are conducted to demonstrate the effectiveness of the proposed procedure.