  This study investigates the estimation and the statistical inference about
Conditional Average Treatment Effects (CATEs), which have garnered attention as
a metric representing individualized causal effects. In our data-generating
process, we assume linear models for the outcomes associated with binary
treatments and define the CATE as a difference between the expected outcomes of
these linear models. This study allows the linear models to be
high-dimensional, and our interest lies in consistent estimation and
statistical inference for the CATE. In high-dimensional linear regression, one
typical approach is to assume sparsity. However, in our study, we do not assume
sparsity directly. Instead, we consider sparsity only in the difference of the
linear models. We first use a doubly robust estimator to approximate this
difference and then regress the difference on covariates with Lasso
regularization. Although this regression estimator is consistent for the CATE,
we further reduce the bias using the techniques in double/debiased machine
learning (DML) and debiased Lasso, leading to $\sqrt{n}$-consistency and
confidence intervals. We refer to the debiased estimator as the triple/debiased
Lasso (TDL), applying both DML and debiased Lasso techniques. We confirm the
soundness of our proposed method through simulation studies.
