Title: A New and Efficient Debiased Estimation of General Treatment Models by Balanced Neural Networks Weighting Show Chinese title

Title: 一种通过平衡神经网络加权的新颖高效无偏估计方法

Abstract: Estimation and inference of treatment effects under unconfounded treatment assignments often suffer from bias and the `curse of dimensionality' due to the nonparametric estimation of nuisance parameters for high-dimensional confounders. Although debiased state-of-the-art methods have been proposed for binary treatments under particular treatment models, they can be unstable for small sample sizes. Moreover, directly extending them to general treatment models can lead to computational complexity. We propose a balanced neural networks weighting method for general treatment models, which leverages deep neural networks to alleviate the curse of dimensionality while retaining optimal covariate balance through calibration, thereby achieving debiased and robust estimation. Our method accommodates a wide range of treatment models, including average, quantile, distributional, and asymmetric least squares treatment effects, for discrete, continuous, and mixed treatments. Under regularity conditions, we show that our estimator achieves rate double robustness and $\sqrt{N}$-asymptotic normality, and its asymptotic variance achieves the semiparametric efficiency bound. We further develop a statistical inference procedure based on weighted bootstrap, which avoids estimating the efficient influence/score functions. Simulation results reveal that the proposed method consistently outperforms existing alternatives, especially when the sample size is small. Applications to the 401(k) dataset and the Mother's Significant Features dataset further illustrate the practical value of the method for estimating both average and quantile treatment effects under binary and continuous treatments, respectively. Show Chinese abstract

Abstract: 在无混淆处理分配下，处理效应的估计和推断通常由于高维混杂因素的非参数扰动参数估计而受到偏差和“维度诅咒”的影响。 尽管已经提出了针对特定处理模型下的二元处理的去偏最先进的方法，但它们在小样本量时可能不稳定。 此外，直接将其扩展到一般处理模型可能导致计算复杂性。 我们提出了一种平衡神经网络权重方法用于一般处理模型，该方法利用深度神经网络缓解维度诅咒，同时通过校准保持最佳协变量平衡，从而实现去偏和稳健的估计。 我们的方法适用于广泛的处理模型，包括离散、连续和混合处理的平均、分位数、分布和非对称最小二乘处理效应。 在常规条件下，我们证明了我们的估计量实现了率双重稳健性和$\sqrt{N}$-渐近正态性，其渐近方差达到了半参数效率界限。 我们进一步开发了一种基于加权引导的统计推断程序，避免了估计有效影响/得分函数。 模拟结果表明，所提出的方法始终优于现有替代方法，尤其是在样本量较小时。 对401(k)数据集和母亲的重要特征数据集的应用进一步说明了该方法在二元和连续处理下估计平均和分位数处理效应的实际价值。