在计量经济学和基因组学中，统计推断的建立往往被混杂变量干扰，造 成伪相关而导致因果关系失真。双去偏 Lasso 方法则旨在有效地估计高维情 形下的隐混杂变量模型，它能同时去除混杂变量和正则化造成的偏差，从而 得到无偏估计。 部分线性模型是一类半参数模型，将线性回归部分和非线性函数同时纳 入其中。以部分线性模型为框架可以方便地同时引入非线性趋势和混杂变量， 符合现实数据分析中面对的大规模非参数或半参数估计中受混杂影响的问题。 本文在受混杂变量影响的部分线性模型的设定下，利用最小二乘估计和 局部线性估计的方法论将模型变形为适用于双去偏 Lasso 方法的形式，再按 照双去偏 Lasso 的算法求解。本文的数值模拟部分在低维和高维情形下分别 进行了实验，研究了新方法受样本量、维数和协变量相关性变化的影响，并得到了不错的结果。

In econometrics and genomics, the establishment of statistical inferences is often distorted by confounding variables that cause pseudo-correlation and lead to distortion of causality. The doubly debiased lasso method, on the other hand, aims to efficiently estimate implicitly confounding variable models in the high-dimensional case by simultaneously removing the bias caused by confounding variables and regularization, resulting in unbiased estimates. Partially linear model is a kind of semiparametric model, including both linear regression and nonlinear functions in itself. Using a partially linear model as a framework allows for the convenient introduction of both nonlinear trends and confounding variables, which is consistent with the problem of large-scale nonparametric or semiparametric estimation under confounding in realistic data analysis. In this paper, in the setting of a partially linear model under confounding, the model is deformed into a form applicable to the doubly debiased lasso using the methodologies of least squares estimation and local linear estimation, and then solved according to the algorithm of doubly debiased lasso. The performance of the new method in the low and high dimensional cases and the influence by changes in sample size, dimensionality and covariate correlations are experimented in the numerical simulation section, and good results are obtained.