characterize semiparametric efficiency

This paper investigates the asymptotic efficiency bound for estimating the average treatment effect (ATE) in binary and multi-treatment sequential experiments under covariate-dependent assignment mechanisms—such as stratification and adaptive designs. Methodologically, it integrates asymptotic statistical theory, stochastic process modeling, and semiparametric efficiency analysis. The key contribution is the first rigorous proof that, under covariate-adaptive allocation, no estimator can achieve first-order asymptotic efficiency exceeding Hahn’s (1998) classical bound. This establishes a unified upper efficiency bound encompassing multi-treatment settings, constrained experimental designs, and covariate-driven single-outcome sampling. The result provides the first general theoretical benchmark for assessing optimality in experimental design and reveals the fundamental theoretical ceiling for design optimization.

This study addresses causal effect estimation in non-i.i.d. sequential experiments, such as AI service evaluations, by establishing the average propensity score as a universal efficiency benchmark for the first time. It reframes efficient experimental design as the problem of learning an optimal allocation rule and proposes two complementary approaches: regression adjustment based on the efficient influence function and an adaptive covariate balancing mechanism. These are integrated with operational constraints to yield a practical batch-adaptive design. Under standard perturbation convergence conditions, the proposed method achieves the semiparametric efficiency bound for linear functionals, attaining sharp second-order convergence rates. Numerical experiments and an evaluation of an AI-powered medical assistant demonstrate that this framework substantially improves estimation efficiency in multi-treatment settings.

Under adaptive data collection, parameter estimation in generalized linear models loses asymptotic normality due to nonparametric nuisance components, hindering valid confidence interval construction. To address this, we propose a weighted estimating equation that systematically corrects adaptive bias. We establish, for the first time, the minimal “explorability” condition required to restore asymptotic normality and guarantee reliable linear functional estimation under weaker assumptions than those in existing literature. Theoretically, our estimator is proven to be asymptotically normal, enabling principled confidence interval construction. Numerical experiments on standard linear bandits and sparse generalized bandits demonstrate both consistency and superior performance relative to state-of-the-art methods, with substantial improvements in estimation accuracy and inference validity.

This paper addresses the problem of efficiently estimating the average treatment effect (ATE) in causal inference. We propose an adaptive experimental design framework with three key contributions: (1) We formally define and dynamically learn the optimal treatment assignment probability that minimizes the semiparametric efficiency bound of the ATE estimator; (2) We introduce the A²IPW estimator, which achieves the theoretically optimal asymptotic variance in finite samples; and (3) We construct nonparametric confidence intervals that are valid at any stopping time, enabling rate-optimal sequential testing and early stopping. The method integrates adaptive randomization, semiparametric efficiency theory, and anytime-valid inference. It substantially reduces the sample size required to achieve a target statistical power while guaranteeing strict coverage probability—even in small-sample settings.

This paper investigates the efficiency of fine-grained stratified randomized experimental designs for estimating generalized moment-based causal parameters—including average, quantile, and local average treatment effects. We propose a design framework that partitions experimental units into fixed-size groups and assigns binary treatments within each group. We establish, for the first time, that the naive moment estimator under this design achieves asymptotically optimal efficiency; we derive a rigorous efficiency lower bound and show that “rapid balancing” is a necessary condition for attaining it. Leveraging asymptotic statistical theory and regular estimator analysis, we demonstrate that this estimator achieves precision comparable to sophisticated post-hoc covariate adjustment methods—without requiring any such adjustment. Its optimality arises intrinsically from the experimental design itself. The core contribution is the formal establishment of fine-grained stratified design as an efficient, parsimonious, and design-driven paradigm for causal inference.

This study addresses partial identification of the complier intensive-margin treatment effect in the presence of endogenous treatment assignment and nonrandom sample selection. By introducing a weak sample selection monotonicity assumption, the paper derives sharper bounds than those in Chen and Flores (2015). It further combines semiparametric orthogonal moment conditions with debiased machine learning to achieve root-n consistent and asymptotically efficient inference, even with high-dimensional covariates or flexible functional forms. Simulation evidence demonstrates favorable finite-sample performance, and empirical applications to the Job Corps and Oregon Health Insurance Experiment substantially tighten both the identified bounds and confidence intervals for the treatment effect.

This work addresses the lack of intuitive geometric interpretation in classical semiparametric efficiency theory, which has hindered the derivation and understanding of influence functions. The paper reformulates the theory within a differential geometric framework on the space of probability distributions, drawing an analogy to multivariate calculus: statistical paths, scores, and influence functions correspond respectively to curves, velocity vectors, and gradients. It demonstrates that the efficient influence function arises naturally as an orthogonal projection. By integrating functional analysis, differential geometry, and statistical inference, the study establishes a unified geometric interpretation of scores, tangent spaces, nuisance tangent spaces, and efficient influence functions. This synthesis not only clarifies several foundational theoretical issues but also substantially enhances the interpretability of methods in causal inference and missing data analysis.

This work addresses the suboptimal inference in semiparametric estimation caused by estimation errors in nuisance functions when using black-box machine learning models. The authors propose a novel estimator that, without imposing additional assumptions, eliminates first-order stochastic errors from nuisance estimation and achieves optimal convergence rates even when auxiliary functions cannot be consistently estimated. Built upon the framework of orthogonal scores and semiparametric linear functionals, the proposed estimator attains the sharp rate \(n^{-1/2} + \delta^a_\mu + (\delta^s_\mu)^2\) and is shown to be asymptotically normal with minimal asymptotic variance. Its tuning strategy favors undersmoothing and substantially outperforms classical double machine learning methods, making it well-suited for widespread applications such as average treatment effect estimation.