debiased jacobian estimation

To address the low estimation accuracy of the average treatment effect (ATE) under high-dimensional covariates (where (p gg n^{1/2})) in completely randomized experiments, this paper proposes a higher-order regression adjustment method based on the Neumann series expansion within a design-based finite-population framework. The method requires no parametric modeling assumptions and relies solely on randomization inference, achieving asymptotic improvement over ordinary least squares (OLS) regression adjustment via a (d)-th order Neumann correction. Theoretically, the corrected estimator is asymptotically normal provided (p^{d+3}(log p)^{d+1} = o(n^{d+2}))—a substantially weaker dimensionality constraint than existing conditions such as (p = o(n^{1/2})) or (o(n^{2/3})). This result breaks a fundamental theoretical bottleneck in ATE estimation under high-dimensional settings and extends the applicability of regression adjustment to ultrahigh-dimensional scenarios.

This paper addresses complex causal problems—such as interference—that resist conventional experimental design, by proposing a unified functional-space framework for causal inference. Methodologically, it systematically introduces the Riesz representation theorem for the first time in this context, modeling causal effects as linear functionals on potential outcome functions and encoding prior assumptions via the structure of function spaces. This enables principled, unified modeling across diverse causal settings. Theoretically, the paper establishes necessary and sufficient conditions for unbiasedness, consistency, and asymptotic normality of the proposed estimators. Computationally, it constructs a new class of estimators with rigorous statistical guarantees and provides a computable conservative variance estimator, enabling reliable confidence interval construction. Overall, the framework furnishes a rigorous functional-analytic foundation for design-driven causal inference.

Accurate estimation and inference for the average treatment effect (ATE) in multi-covariate randomized controlled trials (RCTs) remain challenging, particularly under high-dimensional covariates and small sample sizes. Method: Building on the Neyman finite-population framework, we propose a bias-corrected regression-adjustment estimator with cross-fitting and introduce, for the first time, an HC3-type heteroskedasticity-robust standard error tailored to high-dimensional settings. We rigorously derive first- and second-order stochastic expansions of the random component of regression-adjustment estimators, identifying the source of higher-order bias in conventional inference; leveraging this insight, we design a cross-fitting procedure to eliminate bias and extend HC3 standard errors to stratified experimental designs. Results: Simulations and reanalysis of Angrist et al. (2009)’s education RCT demonstrate that our method substantially improves estimation accuracy, confidence interval coverage, and statistical power—especially in small-sample and high-dimensional scenarios.

This study addresses the efficient and accurate estimation of Riesz representers in debiased machine learning to enable robust inference of causal and structural parameters. To this end, it proposes the Generalized Riesz Regression (GRR) framework, which, for the first time, incorporates Bregman divergence minimization into representer modeling, thereby unifying approaches based on squared loss and KL divergence. Under suitable conditions, GRR automatically achieves covariate balance and Neyman orthogonality without requiring separate estimation of nuisance regression functions. The method integrates modeling in both reproducing kernel Hilbert spaces (RKHS) and neural networks, supported by duality analysis and density ratio estimation techniques, and provides convergence guarantees for both model classes. An open-source Python package, grr, is released to facilitate flexible and efficient Riesz representer estimation.

This paper addresses statistical inference for smooth functionals of nonparametric M-estimators—such as causal effects, quantiles, and survival functions—by proposing the autoDML framework, which automates debiasing without manual influence function derivation. Methodologically, it introduces the first fully automated influence function construction mechanism, integrating gradient/Hessian estimation of the loss, Riesz representer learning, joint risk minimization, and targeted minimum loss estimation; it supports vector-valued M-estimators and Neyman-orthogonal losses. Theoretically, autoDML ensures double robustness and robustness to model misspecification, achieving semiparametric efficiency and second-order bias suppression under quadratic risk. Empirically, it is validated on long-term survival probability estimation in a semiparametric beta-geometric model, demonstrating substantial improvements in both inferential accuracy and automation.

This study addresses the bias arising from estimation errors in nuisance parameters within parametric moment condition models. To mitigate this issue, the paper proposes a high-order debiasing method that constructs moment functions exhibiting Neyman orthogonality of a specified order with respect to the nuisance parameters, thereby substantially reducing the sensitivity of the estimator to such errors. The approach is both unified and computationally tractable, with a key innovation being that the number of additional nuisance parameters required for orthogonality does not grow with the order of orthogonality—indeed, it can be reduced to a single scalar. Theoretical analysis and empirical evidence demonstrate that this method effectively diminishes estimation bias and significantly enhances robustness and precision across a broad class of econometric models.

This study addresses the inferential challenges posed by regularization bias in nonparametric random coefficient models, where dense grids reduce approximation error but introduce bias that undermines valid inference on average functionals—such as mean willingness-to-pay or elasticities. Building on the penalized fixed-grid estimator of Heiss et al., the paper proposes a novel inference framework that centers the estimator around a penalized pseudo-true value and explicitly corrects for regularization-induced bias, thereby enabling asymptotically normal inference for both linear and nonlinear average functionals. This approach is the first to simultaneously leverage the precision of dense grids while effectively accounting for regularization bias, allowing for more flexible and economically interpretable model specifications. Monte Carlo simulations demonstrate that the resulting confidence intervals exhibit accurate finite-sample coverage and informativeness, and empirical analysis reveals that nonparametric specifications can yield substantively different economic conclusions compared to parametric alternatives.

This study addresses the incidental parameter problem arising in panel and network data, where numerous imprecisely estimated nuisance parameters induce severe estimation bias. To mitigate this issue, the proposed method integrates likelihood modeling, Neyman orthogonality theory, and subspace projection techniques. By comparing three distinct notions of orthogonality, this work develops a nested subspace projection approach for constructing orthogonal moments, yielding estimating equations that are robust to nuisance parameter perturbations. The primary contribution lies in providing explicit construction schemes for orthogonal moments across binary choice, count, and nonlinear regression models. Collectively, these advances establish a systematic theoretical framework and practical toolkit for robust statistical inference under high-dimensional, complex data structures.

This study addresses the challenge of constructing Neyman-orthogonal scores for robust causal inference in semiparametric models with infinite-dimensional nuisance parameters. The authors propose a general framework that, for the first time, explicitly constructs orthogonal scores for a broad class of such models, yielding estimators of the target parameter that are asymptotically normal and require only a convergence rate of $o_p(n^{-1/4})$ or better for the nuisance parameter estimates. The approach seamlessly integrates with machine learning algorithms and is applied to estimate causal effects under binary instrumental variables. Numerical experiments demonstrate substantial finite-sample improvements over naive estimators, and an empirical analysis of the Oregon Health Insurance Experiment confirms the method’s robustness and practical utility in real-world settings.

本文提出了一种基于经验似然和协变量平衡约束的方法，在随机实验中调整协变量的同时保持估计量的单调性，提高了估计效率。