stabilized hoif estimators

This work addresses the computational and numerical challenges that commonly arise in practical implementations of higher-order influence function estimation, which often suffer from high-dimensional density estimation or inversion of large Gram matrices. The authors propose a stabilized estimation procedure that eliminates the need for sample splitting by incorporating Gram matrix regularization and a bilinear form structure. This approach avoids high-dimensional density estimation altogether while substantially improving numerical stability in finite samples. The method retains the theoretically optimal convergence rate and provides strong statistical guarantees alongside robust empirical performance, effectively overcoming key limitations of existing higher-order influence function estimators.

To address the low precision of average treatment effect (ATE) estimation in randomized controlled trials (RCTs) with high-dimensional covariates (p ≫ n), this paper proposes a novel covariate adjustment method based on higher-order influence functions (HOIFs). The method systematically establishes the theoretical advantages of HOIFs in RCTs for the first time, unifies a broad class of state-of-the-art adjusted estimators, and rigorously characterizes the conditions under which HOIF-based estimation strictly dominates both unadjusted and linear-model-adjusted estimators. We prove that the proposed estimator achieves semiparametric asymptotic efficiency—i.e., it attains the semiparametric efficiency bound under mild regularity conditions. Numerical simulations and empirical analyses demonstrate substantial gains in estimation accuracy and robustness when p is large relative to n. An accompanying R package, implementing the method, has been publicly released on CRAN.

This work addresses the suboptimal convergence rates of classical influence functions when estimating complex, implicitly defined causal parameters such as quantile treatment effects. While existing higher-order methods are limited to explicitly defined parameters, this paper extends the higher-order influence function framework to implicit M- and Z-estimation problems for the first time. By integrating U-process theory with nonparametric estimation, the authors construct a debiased estimator that substantially relaxes the stringent Hölder smoothness assumptions typically imposed on nuisance parameters. The proposed approach achieves improved convergence rates in settings like quantile treatment effect estimation and reduces requirements on model complexity, thereby broadening the applicability of higher-order influence function methodology to a wider class of semiparametric problems.

This paper addresses the problem of estimating functionals of an unknown target function under a structure-agnostic setting—where no specific structural assumptions (e.g., Hölder smoothness) are imposed on the nuisance function, and only a generic convergence rate for nuisance estimation is assumed. Methodologically, it introduces the first formal framework for structure-agnostic estimation, operating under three simultaneous constraints: weak regularity conditions, compatibility with general-purpose nuisance estimators, and sample splitting. Theoretically, it establishes, for the first time, the essential optimality of first-order debiased estimators in this setting. Through minimax lower bound analysis, higher-order perturbation theory, and a unified debiasing framework, the paper precisely characterizes the optimal convergence rate and quantifies the fundamental trade-off between incorporating structural priors and improving estimation efficiency. These results provide foundational theoretical support for nonparametric and semiparametric inference.

In structural estimation, objective functions are often noisy, nonsmooth, and nonconvex, causing conventional optimization methods to readily converge to local minima and hindering rigorous characterization of statistical properties. To address this, we propose a hybrid algorithm integrating an enhanced Gauss–Newton method with adaptive grid search: grid search ensures robust global exploration in early stages, followed by a seamless transition to the improved Gauss–Newton method for rapid local convergence. For the first time under purely econometric assumptions—without restrictive smoothness or convexity conditions—we simultaneously establish finite-sample optimization error bounds and the asymptotic distribution of the estimator. Simulation studies and empirical applications demonstrate that our method substantially improves estimation accuracy and convergence stability, attaining the true solution with high probability while avoiding exhaustive search. It thus achieves an optimal trade-off between computational efficiency and statistical reliability.

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.

研究通过放宽可识别性要求，使用惩罚最小二乘法从一系列嵌套类中选择回归模型的阶数，解决了在误差依赖和非可识别情况下的一致阶数选择问题。

This study investigates the asymptotic admissibility of Double Machine Learning (DML) estimators for quadratic functionals and integral functionals of densities under structural agnosticism. By integrating higher-order influence functions (HOIF), U-statistic theory, and a structure-free modeling framework, the authors establish—for the first time—that DML is asymptotically inadmissible for these two classes of functionals and construct a second-order influence function estimator that asymptotically dominates DML. For a third class of functionals, both DML and HOIF estimators achieve minimax optimality but neither dominates the other. These findings reveal fundamental limitations of DML under weak structural assumptions and provide superior alternatives grounded in higher-order influence functions.

This study addresses the problem of efficiently computing unbiased estimators for high-order U-statistics, such as distance covariance and HSIC. By establishing the equivalence between U-centering and the residual structure in ANOVA, the authors propose a generalized high-order U-centering framework: symmetric hollow arrays are interpreted as least-squares residuals after fitting additive endpoint effects, and this perspective is extended to r-tuple subset indexing to eliminate lower-order effects involving fewer than r sample labels. This approach unifies high-order Hoeffding decompositions with variance component estimation, yielding an unbiased estimator with O(n^r) computational complexity. The method accurately computes inner products of r-th order Hoeffding components and expresses the highest-order variance component as a non-negative mean squared residual, substantially enhancing both computational efficiency and theoretical clarity.

Traditional influence functions fail in constrained learning settings because they neglect how data perturbations affect the feasible region, leading to biased estimates or infeasible solutions. This work proposes Directional Influence Functions (DIF), which explicitly incorporate constraints into the influence analysis framework for the first time. By modeling the optimality conditions of constrained optimization as a variational inequality and integrating sensitivity analysis with leave-one-out approximations, DIF accurately captures the effect of training sample perturbations on model parameters. Experiments on constrained linear regression and CNNs with fairness constraints demonstrate that DIF precisely replicates retraining results, significantly outperforming classical influence functions and their penalty-based variants, and exhibits strong alignment with actual retraining outcomes in predicting changes in test loss.