Estimating the marginally adjusted dose-response curve for continuous treatments is a longstanding statistical challenge critical across multiple fields. In the context of parametric models, mis-specification may result in substantial bias, hindering the accurate discernment of the true data generating distribution and the associated dose-response curve. In contrast, non-parametric models face difficulties as the dose-response curve isn't pathwise differentiable, and then there is no $\sqrt{n}$-consistent estimator. The emergence of the Highly Adaptive Lasso (HAL) MLE by van der Laan [2015] and van der Laan [2017] and the subsequent theoretical evidence by van der Laan [2023] regarding its pointwise asymptotic normality and uniform convergence rates, have highlighted the asymptotic efficacy of the HAL-based plug-in estimator for this intricate problem. This paper delves into the HAL-based plug-in estimators, including those with cross-validation and undersmoothing selectors, and introduces the undersmoothed smoothness-adaptive HAL-based plug-in estimator. We assess these estimators through extensive simulations, employing detailed evaluation metrics. Building upon the theoretical proofs in van der Laan [2023], our empirical findings underscore the asymptotic effectiveness of the undersmoothed smoothness-adaptive HAL-based plug-in estimator in estimating the marginally adjusted dose-response curve.

翻译：针对连续治疗的边际调整剂量-响应曲线的估计是一个长期存在的统计学难题，在多个领域具有关键意义。在参数模型框架下，模型设定错误可能导致显著偏差，从而阻碍对真实数据生成分布及相关剂量-响应曲线的准确识别。相比之下，非参数模型面临困难，因为剂量-响应曲线不具备路径可微性，因而无法获得$\sqrt{n}$相合估计量。van der Laan [2015]与van der Laan [2017]提出的高适应Lasso（HAL）极大似然估计量，以及van der Laan [2023]后续关于其逐点渐近正态性与一致收敛速率的理论证明，凸显了基于HAL的插件估计量在这一复杂问题中的渐近有效性。本文深入探讨基于HAL的插件估计量，包括采用交叉验证与欠平滑选择器的变体，并引入基于欠平滑自适应光滑度HAL的插件估计量。我们通过大量模拟实验，运用详尽的评估指标对这些估计量进行系统评估。基于van der Laan [2023]的理论证明，我们的实证研究结果进一步证实了欠平滑自适应光滑度HAL插件估计量在估计边际调整剂量-响应曲线方面的渐近有效性。