In the problem of estimating target parameters in nonparametric models with nuisance parameters, substituting the unknown nuisances with nonparametric estimators can introduce "plug-in bias." Traditional methods addressing this sub-optimal bias-variance trade-offs rely on the influence function (IF) of the target parameter. When estimating multiple target parameters, these methods require debiasing the nuisance parameter multiple times using the corresponding IFs, posing analytical and computational challenges. In this work, we leverage the targeted maximum likelihood estimation framework to propose a novel method named kernel debiased plug-in estimation (KDPE). KDPE refines an initial estimate through regularized likelihood maximization steps, employing a nonparametric model based on reproducing kernel Hilbert spaces. We show that KDPE (i) simultaneously debiases all pathwise differentiable target parameters that satisfy our regularity conditions, (ii) does not require the IF for implementation, and (iii) remains computationally tractable. We numerically illustrate the use of KDPE and validate our theoretical results.

翻译：在有 nuisance 参数的非参数模型中估计目标参数时，用非参数估计量替代未知 nuisance 参数会引入“插件偏差”。传统方法通过依赖目标参数的影响函数来应对这种次优的偏差-方差权衡。当估计多个目标参数时，这些方法需要使用相应的 IF 对 nuisance 参数多次去偏，从而带来分析和计算上的挑战。本研究利用目标最大似然估计框架，提出了一种名为“核去偏插件估计”（KDPE）的新方法。KDPE 通过正则化似然最大化步骤优化初始估计，并采用基于再生核希尔伯特空间的非参数模型。我们证明 KDPE 能够：（i）同时对所有满足正则性条件的路径可微目标参数进行去偏；（ii）在实施中无需 IF；（iii）保持计算可行性。我们通过数值实验展示了 KDPE 的应用，并验证了理论结果。