one-step likelihood estimation

This study addresses the failure of standard influence function–based inference in finite samples under “near-boundary” settings of semiparametric models, where second-order remainder terms non-negligibly contribute to sampling variance. The authors propose a finite-sample variance decomposition framework that separates influence function variance from remainder-induced variance and establish necessary and sufficient conditions for the consistency of sandwich variance estimators. Building on this framework, they develop two robust variance estimators—the leave-one-unit-out jackknife and a paired-cluster bootstrap—and derive an analytical expression for the interaction between remainder terms and within-cluster correlation in clustered data. Their approach enables valid confidence interval construction near the boundary: the jackknife Wald interval is numerically equivalent to a bias-corrected sandwich estimator and accurately captures the mechanism by which clustering amplifies variance estimation bias.

Constructing efficient debiased estimators traditionally requires manual derivation of the efficient influence function (EIF), a labor-intensive process with high technical barriers and poor scalability. Method: This paper introduces Dimple, the first framework that models statistical functionals as compositions of differentiable primitives satisfying a novel differentiability condition; it leverages automatic differentiation to directly generate unbiased, efficient estimators while simultaneously identifying nuisance parameters. Dimple integrates probabilistic programming with functional decomposition, eliminating the need for explicit EIF derivation. Contribution/Results: We provide an open-source Python library enabling users to define parameters, generate estimators, and perform inference in just a few lines of code. Extensive experiments demonstrate Dimple’s effectiveness across diverse causal and semiparametric models—including AIPW, DR-Learner, and doubly robust IV—significantly lowering the barrier to constructing efficient estimators without sacrificing statistical efficiency.

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.

For stochastic simulation models with intractable likelihoods, existing score estimators based on noisy Monte Carlo ratio estimators suffer from bias and instability. Method: We propose the first gradient-based simulation parameter estimation framework, which eliminates ratio bias via a multi-timescale stochastic approximation algorithm, incorporates a nested simulation optimization architecture, and extends— for the first time—to neural network training. The method integrates stochastic approximation, multiscale optimization, nested Monte Carlo estimation, and asymptotic statistical analysis. Contributions/Results: We rigorously establish strong consistency, asymptotic normality, optimal convergence rate, and an optimal budget allocation strategy for the estimator. Numerical experiments demonstrate substantial improvements in estimation accuracy and significant reductions in computational cost.

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.

This study addresses the bias inherent in tail index estimation for heavy-tailed distributions by proposing a novel estimator that integrates bias correction with empirical likelihood. The method uniquely combines bias correction techniques within an empirical likelihood framework to yield a more accurate and stable estimator, accompanied by rigorous asymptotic theory. Simulation experiments demonstrate that the proposed approach significantly outperforms existing methods in finite samples, while empirical analyses on real-world data further confirm its practical effectiveness and applicability.

This study addresses Bayesian inference for low-dimensional target parameters in semiparametric models, particularly under the presence of complex nuisance components that may compromise frequentist properties. To this end, we construct posterior distributions by integrating estimating function methods with nonparametric Bayesian techniques—such as Dirichlet processes and Bayesian bootstrap—under conditions weaker than the classical stochastic equicontinuity assumption. We establish asymptotic normality and consistency of the resulting posterior, rigorously identifying the key assumptions required to guarantee desirable frequentist behavior. The theoretical analysis systematically elucidates how relaxing these assumptions affects inferential performance. Extensive simulations corroborate the effectiveness of the proposed methodology, demonstrating its robustness and accuracy in practical settings.

This study investigates the frequentist validity of two-step (plug-in) approaches in semiparametric Bayesian inference, with particular emphasis on settings involving nuisance parameters. For models satisfying Neyman orthogonality conditions, the authors demonstrate that marginal posteriors for the target parameter retain desirable frequentist properties—even when uncertainty in estimating the nuisance parameters is ignored—by effectively severing feedback between the nuisance and target parameters. The analysis is further extended to non-orthogonal settings, where posterior asymptotic robustness is guaranteed under mere consistency of the nuisance parameter estimator. Methodologically, the framework combines Dirichlet processes with Bayesian bootstrap techniques for nonparametric modeling and is applied to plug-in estimation of propensity scores in causal inference, showing that the plug-in step exerts negligible influence on the resulting posterior for the target parameter.

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.

Existing median bias correction methods are often implicit, computationally intensive, and rely on fully specified perturbation parameters, limiting their applicability under parameter transformations. This work proposes an explicit, general third-order median-unbiased estimator for smooth scalar transformations of a reference parameter. Building on the Cornish–Fisher expansion, the method directly constructs a higher-order approximation to the centered maximum likelihood estimator without solving nonlinear systems. It requires only the maximum likelihood estimate, its gradient and Hessian, and expectations of products of log-likelihood derivatives—obtainable analytically or via Monte Carlo simulation. The approach accommodates arbitrary smooth transformations, integrates naturally with hull confidence intervals, and achieves near-nominal finite-sample coverage in regression, circular, and hierarchical models. It has been successfully applied to post-selection inference after FIC, Mahalanobis distances, and quantile estimation.