The partially linear model (PLM) is a useful semiparametric extension of the linear model that has been well studied in the statistical literature. This paper proposes a variable selection procedure for the PLM with ultrahigh dimensional predictors. The proposed method is different from the existing penalized least squares procedure in that it relies on partial correlation between the partial residuals of the response and the predictors. We systematically study the theoretical properties of the proposed procedure and prove its model consistency property. We further establish the root-n convergence of the estimator of the regression coefficients and the asymptotic normality of the estimate of the baseline function. We conduct Monte Carlo simulations to examine the finite-sample performance of the proposed procedure and illustrate the proposed method with a real data example.

中文翻译：

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通过偏相关选择部分线性模型的变量

部分线性模型 (PLM) 是线性模型的一种有用的半参数扩展，已在统计文献中得到充分研究。本文为具有超高维预测器的 PLM 提出了一种变量选择程序。所提出的方法不同于现有的惩罚最小二乘程序，因为它依赖于响应的部分残差和预测变量之间的部分相关性。我们系统地研究了所提出程序的理论特性并证明了其模型一致性特性。我们进一步建立了回归系数估计量的 n 根收敛性和基线函数估计量的渐近正态性。