In causal inference about two treatments, Conditional Average Treatment
Effects (CATEs) play an important role as a quantity representing an
individualized causal effect, defined as a difference between the expected
outcomes of the two treatments conditioned on covariates. This study assumes
two linear regression models between a potential outcome and covariates of the
two treatments and defines CATEs as a difference between the linear regression
models. Then, we propose a method for consistently estimating CATEs even under
high-dimensional and non-sparse parameters. In our study, we demonstrate that
desirable theoretical properties, such as consistency, remain attainable even
without assuming sparsity explicitly if we assume a weaker assumption called
implicit sparsity originating from the definition of CATEs. In this assumption,
we suppose that parameters of linear models in potential outcomes can be
divided into treatment-specific and common parameters, where the
treatment-specific parameters take difference values between each linear
regression model, while the common parameters remain identical. Thus, in a
difference between two linear regression models, the common parameters
disappear, leaving only differences in the treatment-specific parameters.
Consequently, the non-zero parameters in CATEs correspond to the differences in
the treatment-specific parameters. Leveraging this assumption, we develop a
Lasso regression method specialized for CATE estimation and present that the
estimator is consistent. Finally, we confirm the soundness of the proposed
method by simulation studies.

在关于两种处理方法的因果推断中，条件平均处理效应（CATEs）作为一种代表个体因果效应的数量起着重要角色，它被定义为在协变量条件下两种处理方法的期望结果的差异。本研究假设了两个潜在结果与两种处理方法的协变量之间的线性回归模型，并将 CATEs 定义为这两个线性回归模型之间的差异。我们提出了一种方法，用于在高维度和非稀疏参数下一致地估计 CATEs。通过假设 CATEs 的隐式稀疏性，我们展示了理论上的一致性等理想性质的实现性，即使不显式假定稀疏性。利用这种假设，我们开发了一种专门用于 CATE 估计的 Lasso 回归方法，并证明了估算量的一致性。最后，我们通过模拟研究确认了所提出方法的合理性。