Debiased Ill-Posed Regression
去偏的病态回归估计AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要明确列举非参数工具变量结构函数估计与近端因果推断桥函数估计，分别支持结构估计和因果推断分类。
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去偏的病态回归估计
- 研究问题
- 当目标函数仅由条件矩限制约束时，如何降低干扰函数估计缓慢或误设的影响，并控制病态问题中的估计误差？
- 方法与思路
- 作者基于修正投影误差的影响函数构造去偏估计，使用交叉验证选择超参数，并分析函数估计及线性泛函估计的误差。
- 材料陈述的贡献
- 摘要称估计量具有关于干扰函数的二阶偏差和特定误设稳健性，给出有限样本界、调参误差界及根号样本量一致的充分条件。
- 阅读关注点
- 应核对条件矩算子的病态程度、误设稳健性对应哪个干扰函数，以及交叉验证造成的速率损失和规则参数的条件。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未核实；摘要未给出具体误差界或正则条件，不能将稳健性理解为任意误设下有效。
原文摘要
In various statistical settings, the goal is to estimate a function which is restricted by the statistical model only through a conditional moment restriction. Prominent examples include the nonparametric instrumental variable framework for estimating the structural function of the outcome variable, and the proximal causal inference framework for estimating the bridge functions. A common strategy in the literature is to find the minimizer of the projected mean squared error. However, this approach can be sensitive to misspecification or slow convergence rate of the estimators of the involved nuisance components. In this work, we propose a debiased estimation strategy based on the influence function of a modification of the projected error and demonstrate its finite-sample convergence rate. Our proposed estimator possesses a second-order bias with respect to the involved nuisance functions and a desirable robustness property with respect to the misspecification of one of the nuisance functions. The proposed estimator involves a hyper-parameter, for which the optimal value depends on potentially unknown features of the underlying data-generating process. Hence, we further propose a hyper-parameter selection approach based on cross-validation and derive an error bound for the resulting estimator. This analysis highlights the potential rate loss due to hyper-parameter selection and underscore the importance and advantages of incorporating debiasing in this setting. We also study the application of our approach to the estimation of regular parameters in a specific parameter class, which are linear functionals of the solutions to the conditional moment restrictions and provide sufficient conditions for achieving root-n consistency using our debiased estimator.