ROSE随机森林用于稳健半参数有效估计
ROSE Random Forests for Robust Semiparametric Efficient Estimation
AI总结：
针对半参数有效估计在实践中难以实现的问题，提出ROSE随机森林估计器，通过估计最优权重实现稳健半参数效率，在模拟和真实数据上验证了有效性。
摘要：
人们普遍认识到，半参数有效估计在实践中难以实现：理论上有效的估计器可能需要对复杂干扰函数的估计达到难以企及的精度水平。因此，在实际数据集上部署的估计器往往以某种临时方式选择，并可能遭受高方差。我们在包括广义部分线性模型在内的广泛半参数回归模型集合背景下，研究了理论与实践的差距。我们提倡使用稳健的估计器，其含义是：在由用户选择的机器学习方法可估计的某些条件期望所表征的足够丰富的分布类上，估计器具有一致性的$\sqrt{n}$收敛速度。我们证明，即使要求在该类内进行局部一致估计，也会将可能的估计器缩小到由某些权重函数参数化的那些估计器。相反，我们证明此类估计器确实提供了所需的统一一致性，并引入了一种新颖的基于随机森林的程序来估计最优权重。我们证明所得估计器恢复了稳健半参数效率（ROSE）的概念，并为半参数有效估计器提供了实用的替代方案。我们在模拟和真实数据上的多种半参数设置中展示了我们的ROSE随机森林估计器的有效性。
英文摘要：
It is widely recognised that semiparametric efficient estimation can be hard to achieve in practice: estimators that are in theory efficient may require unattainable levels of accuracy for the estimation of complex nuisance functions. As a consequence, estimators deployed on real datasets are often chosen in a somewhat ad hoc fashion, and may suffer high variance. We study this gap between theory and practice in the context of a broad collection of semiparametric regression models that includes the generalised partially linear model. We advocate using estimators that are robust in the sense that they enjoy $\sqrt{n}$-consistent uniformly over a sufficiently rich class of distributions characterised by certain conditional expectations being estimable by user-chosen machine learning methods. We show that even asking for locally uniform estimation within such a class narrows down possible estimators to those parametrised by certain weight functions. Conversely, we show that such estimators do provide the desired uniform consistency and introduce a novel random forest-based procedure for estimating the optimal weights. We prove that the resulting estimator recovers a notion of $\textbf{ro}$bust $\textbf{s}$emiparametric $\textbf{e}$fficiency (ROSE) and provides a practical alternative to semiparametric efficient estimators. We demonstrate the effectiveness of our ROSE random forest estimator in a variety of semiparametric settings on simulated and real-world data.
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