apply cross-fitting procedures

This work addresses the challenges of achieving efficient semiparametric estimation of low-dimensional target parameters in the presence of high-dimensional nuisance functions, where out-of-sample prediction of nuisances and statistical efficiency are critical concerns. The authors propose a general, estimator-agnostic cross-fitting engine that automatically executes reproducible folding schedules based on user-specified target functionals and a directed acyclic graph (DAG) encoding the nuisance model structure. Innovatively leveraging graph-based nuisance modeling, the framework supports folding strategies such as disjointness and independence enhancement, while reducing branching dependencies through node replication. It further incorporates explicit scheduling, dependency validation, intelligent caching, and fault isolation mechanisms. Implemented as a lightweight R package publicly available on CRAN, this approach substantially improves the controllability, reproducibility, and computational efficiency of cross-fitting estimators, facilitating large-scale simulations and rapid prototyping.

This study addresses the severe undercoverage of confidence intervals when estimating population average treatment effects using flexible machine learning models under complex survey designs, such as stratified multistage sampling. The authors propose a survey-weighted targeted maximum likelihood estimator (TMLE) with cross-fitting implemented at the primary sampling unit (PSU) level, combined with Taylor linearization of the influence function to obtain design-consistent variance estimates. Theory and simulations demonstrate for the first time that valid inference requires cross-fitting specifically at the PSU level—internal cross-validation is insufficient. In NHANES-like simulations, the proposed method achieves stable coverage of 93%–95%, substantially outperforming single-fit TMLE (as low as 22%) and internal cross-validation (85%–88%). Empirical analyses of four NHANES datasets confirm its practical utility, and accompanying open-source software has been released.

This study addresses the power loss of conventional variance estimators under alternative hypotheses, where residual drift causes test power to vanish at distant alternatives. To overcome this limitation, it proposes a cross-fitting variance estimation framework that leverages auxiliary linear combinations to eliminate bias induced by residual drift, while precisely characterizing conditional bias to establish estimator consistency under the alternative. This framework generalizes to variance estimation in econometric testing scenarios involving nonparametric specifications, overidentification, and multiple restrictions. Both theoretical analysis and empirical application to the Oregon Health Insurance Experiment demonstrate that the proposed approach substantially enhances the power of quadratic-form test statistics.

To address low data utilization and unstable inference results caused by sample splitting in predictive model evaluation and causal inference, this paper proposes a novel inferential framework based on multiple splitting and cross-fitting. Theoretically, we establish a central limit theorem for multi-split estimators applicable to arbitrarily complex models, and develop asymptotic variance estimation and confidence interval construction that explicitly account for dependence across splits. Methodologically, we introduce a new criterion quantifying *p*-value reproducibility across splits to enhance the reliability of statistical inference. Empirical applications—including poverty alleviation prediction and heterogeneous treatment effect estimation—demonstrate that the proposed method substantially improves statistical power: it detects significant effects missed by conventional single-split approaches while maintaining robustness, generality, and practical applicability.

Traditional linear-model t/F-tests assume fixed sample sizes, rendering them unsuitable for sequential A/B testing requiring continuous monitoring and early stopping—leading to uncontrolled Type-I error inflation. This paper proposes an anytime-valid causal inference framework under linear regression adjustment, introducing the first closed-form anytime-valid F-tests and confidence sequences for both parametric and nonparametric settings. Without imposing strong modeling assumptions, the method guarantees uniform Type-I error control and valid confidence coverage throughout the entire sequential experiment under standard randomized designs. All test statistics are directly computable from standard regression outputs, enabling real-time significance assessment and dynamic confidence interval updating. Deployed on Netflix’s industrial-scale A/B testing platform, the method supports regression-adjusted sequential analysis using pre-treatment covariates, effectively mitigating p-hacking.

研究使用五折交叉拟合和机器学习方法（如随机森林和梯度提升机）估计响应倾向，以改进调查估计中的无应答调整问题。

本文探讨了使用样条函数近似条件期望和倾向得分函数的半参数方法来解决多值处理下的污染偏差问题。

This study addresses the problem of insufficient confidence interval coverage in cross-fitting under non-regular settings, where cross-fold correlation undermines inferential validity. By establishing a central limit theorem grounded in locality conditions, this work reveals the asymptotic normality of cross-fitted estimators despite non-regularity. Furthermore, it introduces a novel method for estimating cross-fold correlation to correct the asymptotic variance, integrating random forests and neural networks to facilitate valid statistical inference. The primary contribution lies in theoretically quantifying and adjusting for the impact of cross-fold dependence. Simulation experiments demonstrate that the proposed approach achieves near-nominal coverage rates across diverse models, substantially enhancing the reliability of machine learning-based inference in non-regular scenarios.

本文提出了一种邻域排除交叉拟合方法，以解决网络干扰下的无偏处理效应估计问题，确保在有限样本下保持无偏性。

This study addresses the sensitivity of conventional maximum likelihood estimation to outliers in modeling proportion data with boundary values, which often leads to biased inference. To overcome this limitation, the authors propose a robust inflated Beta regression estimator that exhibits strong robustness and favorable asymptotic properties. A Wald-type robust test is developed alongside the estimator, and a data-driven adaptive tuning algorithm is introduced to enhance performance. The proposed approach significantly improves robustness while preserving model simplicity and interpretability. Extensive simulations and empirical analyses demonstrate that the method substantially outperforms traditional maximum likelihood estimation in the presence of outliers, offering both theoretical rigor and practical utility.