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Invariant quantile regression for heterogeneous environments

异质环境下的不变量分位数回归

In this paper, we propose an invariant quantile regression (IQR) framework specifically designed for multi-environment datasets, which captures the invariance across different environments. This framework is closely related to transfer learning, causal inference, and fair machine learning, and is motivated by scenarios in which the conditional probability of the response given covariates varies, while certain key variables remain invariant. This perspective differs notably…

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On the use of auxiliary variables in multiple imputation when estimating the average causal effect with missing data

缺失数据下估计平均因果效应时,多重插补中辅助变量的使用

Estimating the average causal effect (ACE) using observational data is a key focus in causal inference for which missing data present an important challenge. Multiple imputation (MI) is a widely used method for handling missing data and can yield unbiased estimates when the imputation is compatible with the substantive analysis. One of the advantages of MI is its scope to include so-called "auxiliary variables", defined as variables associated with incomplete variables that…

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Local Average and Marginal Treatment Effects with a Misclassified Treatment

处理变量误分类时的局部平均处理效应与边际处理效应

This paper studies identification of the local average and marginal treatment effects (LATE and MTE) with a misclassified binary treatment variable. We derive bounds on the (generalized) LATE and exploit its relationship with the MTE to further bound the MTE. Indeed, under some standard assumptions, the MTE is a limit of the ratio of the variation in the conditional expectation of the observed outcome given the instrument to the variation in the true propensity score, which…

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Fast Nonparametric Conditional Independence Testing via Two-Stage Regression

通过两阶段回归快速进行非参数条件独立检验

Constraint-based causal discovery relies on repeated conditional independence tests, but fast nonparametric tests often sacrifice calibration, especially when variables depend on the conditioning set through nonlinear relationships. We introduce BLITZ (Broad-to-Local Independence Testing via residualiZation), a nonparametric conditional independence test designed to run well under a second while maintaining the accuracy needed for the thousands of queries performed by…

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Deconfounding via Profiled Transfer Learning

通过剖面化迁移学习消除混杂

Unmeasured confounders are a major source of bias in regression-based effect estimation and causal inference. In this paper, we propose a new profiled transfer learning framework, ProTrans, to address confounding effects in the target dataset, when additional source datasets with similar confounding structures are available. We introduce the concept of profiled residuals to characterize the shared confounding patterns between source and target datasets. By incorporating…

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A New Targeted-Federated Learning Framework for Estimating Heterogeneity of Treatment Effects: A Robust Framework with Applications in Aging Cohorts

估计处理效应异质性的目标联邦学习框架:稳健方法与老龄队列应用

Analyzing data from multiple sources offers valuable opportunities to improve the estimation efficiency of causal estimands. However, this analysis also poses many challenges due to population heterogeneity and data privacy constraints. While several advanced methods for causal inference in federated settings have been developed in recent years, many focus on difference-based averaged causal effects and are not designed to study effect modification. In this study, we…

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A Test for Treatment Heterogeneity under a Distributional Difference-in-Difference Framework

分布双重差分框架下的处理异质性检验

We develop a novel distributional Difference-in-Differences (DiD) framework to capture treatment heterogeneity across outcome distributions. By leveraging optimal transport, we use the control group to estimate the untreated distributional drift from the pre- to post-treatment period and apply it to the treated group's pre-treatment baseline, constructing a counterfactual distribution under the assumption of no treatment effect. We frame the null hypothesis as a…

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Privacy-preserving Meta-analysis through Low-Rank Basis Hunting

通过低秩基函数搜寻实现保护隐私的元分析

A central challenge of meta-analysis is that the populations underlying existing studies often differ from the target population in unknown ways. We study the problem of predicting function-valued quantities, such as regression and conditional average treatment effect functions, for a new target population using only study-level covariates and study-specific function estimates. We propose MetaHunt, a new meta-analysis methodology based on a shared low-rank structure, in…

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Estimating Representative Causal Effects with Double Machine Learning

用双重机器学习估计具有总体代表性的因果效应

Double Machine Learning is widely used to estimate treatment effects from non-experimental data. The "residuals-on-residuals" regression (RORR) is especially popular for its simplicity and computational tractability. However, with heterogeneous treatment effects, the proper interpretation of RORR may not be well understood. We show that, for non-binary treatments with continuous dose-response functions, RORR estimates a conditional variance-weighted average of derivatives…

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Design-Based Inference under Random Potential Outcomes

随机潜在结果下的基于设计的推断

We study whether mechanism-level causal estimands, defined as expectations over latent stochastic environments, can be consistently recovered from a single realised randomised experiment. Identification alone does not guarantee recoverability. The target estimand averages over latent environments, whereas a single experiment provides only one realisation of such an environment. We show that suitably sparse local dependence induces an ergodic-type property under which…

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Semi- and non-parametric approaches to individualized treatment regimes in the presence of causal mediation

存在因果中介时个体化治疗规则的半参数与非参数方法

Individualized treatment rules (ITRs) map an individual patient's characteristics to their recommended treatment value. Typically, the optimal ITR is defined as the rule which maximizes a mean counterfactual outcome; the resulting ITR maximizes the effect of treatment along all causal pathways to the outcome, including indirect pathways through mediating variables. Although maximizing the total effect is often sufficient, explicitly incorporating causal mediation in an ITR…

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Randomly Assigned First Differences?

一阶差分真的是随机分配的吗?

We consider a first-difference regression of an outcome evolution $ΔY$ on a treatment evolution $ΔD$. If the treatment effect changes over time, the regression residual is a function of the period-one treatment $D_{1}$. Then, researchers should test if $ΔD$ and $D_{1}$ are correlated: if they are, the regression may suffer from an omitted variable bias. To solve it, researchers may control for $E(ΔD|D_{1})$. We revisit Acemoglu et al (2016), who study the effect of imports…

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What's the Magic Formula Instrument?

“神奇公式工具变量”究竟是什么?

Two recent papers by Borusyak and Hull (2023, 2026) propose using known formulas to adjust linear instrumental variable estimators for confounding covariates. Implementing this "formula instrument" approach requires making a parametric assumption on the distribution of the unobserved shocks that generated the instrument. We develop a method for systematically evaluating the sensitivity of formula instrument estimates to this parametric assumption. The method is…

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Balanced Twins: Causal Inference on Time Series with Hidden Confounding

平衡孪生:存在隐藏混杂的时间序列因果推断

Accurately estimating treatment effects in time series is essential for evaluating interventions in real-world applications, especially when treatment assignment is biased by unobserved factors. In many practical settings, interventions are adopted at different times across individuals, leading to staggered treatment exposure and heterogeneous pre-treatment histories. In such cases, aggregating outcome trajectories across treated units is ill-defined, making individual…

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An Adaptive Online Smoother with Closed-Form Solutions and Information-Theoretic Lag Selection for Conditional Gaussian Nonlinear Systems

条件高斯非线性系统的自适应在线平滑:闭式解与信息论滞后选择

Data assimilation (DA) combines partial observations with dynamical models to improve state estimation. Filter-based DA uses only past and present data and is the prerequisite for real-time forecasts. Smoother-based DA exploits both past and future observations. It aims to fill in missing data, provide more accurate estimations, and develop high-quality datasets. However, the standard smoothing procedure requires using all historical state estimations, which is…

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Measuring the Impact of Missingness in Traffic Stop Data

衡量交通拦查数据中缺失信息的影响

In this article we explore the data available through the Stanford Open Policing Project. The data consist of information on millions of traffic stops across close to 100 different cities and highway patrols. Using a variety of metrics, we identify that the data is not missing completely at random. Furthermore, we develop ways of quantifying and visualizing missingness trends for different variables across the data sets. Because of the way we have identified the missingness…

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Exploiting independence constraints for efficient estimation of bounds on causal effects in the presence of unmeasured confounding

利用独立性约束高效估计未测混杂下的因果效应界

Causal graphs may inform covariate adjustment for estimating causal effects and improve estimation efficiency by exploiting the graphical structure. In many applications, however, the target causal parameter may not be point-identified due to the presence of unmeasured confounding. Sensitivity analysis methods address this challenge by characterizing bounds on the causal parameter under varying assumptions about the magnitude or form of unmeasured confounding. We focus on…

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Benign overfitting beyond prediction: The ordinary least squares interpolator

超越预测的良性过拟合:普通最小二乘插值估计量

Recent advances in deep learning have highlighted the phenomenon of benign overfitting in overparameterized statistical models, sparking significant interest in understanding its foundations. Owing to its simplicity and practical relevance, the ordinary least squares (OLS) interpolator has become a key object of study for gaining theoretical insight into this phenomenon. While the properties of OLS are well understood in classical underparameterized settings, its behavior in…

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Choosing A Headline Estimand from Matching, DID, and Hybrid Designs: A Minimax-Regret Approach

从匹配、双重差分与混合设计中选择主要估计目标:最小最大遗憾方法

Researchers using panel data to estimate causal effects routinely choose among three approaches to using past outcomes: difference-in-differences (DID), conditioning on lagged outcomes (matching, M), and a hybrid that does both (DIDM). The corresponding identifying assumptions are non-nested, leaving little guidance on which to report. We give conditions under which the corresponding estimands are ordered, with DIDM bracketed between matching and DID. This makes DIDM the…

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Private Rate-Double-Robust Inference

局部隐私保护下的速率双重稳健推断

We reconcile privacy protection and rate-double-robust inference. The privacy of individuals is protected by a local privacy mechanism: injecting noise into their sensitive data, revealing only the noisy data for inference. Hence, privacy protection hinders inference. In contrast, the inference of a target parameter is rate-double-robust when the large-sample bias of an estimator of the parameter is characterised by a trade-off between the estimation errors of two other,…

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Anchors Away: Navigating Unanchored Indirect Comparisons with Multilevel Unanchored Meta-Regression (ML-UMR)

多层无锚点元回归:无共同对照的间接治疗比较

Unanchored indirect treatment comparisons using single-arm studies or disconnected evidence are increasingly used in health technology assessment (HTA) when randomized evidence is unavailable. Existing methods, including matching-adjusted indirect comparison (MAIC) and simulated treatment comparison (STC), are generally limited to pairwise settings and typically estimate marginal effects in the comparator study population, which may differ from the decision-relevant…

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Environment-Adaptive Covariate Selection: Learning When to Use Spurious Correlations for Out-of-Distribution Prediction

环境自适应协变量选择:分布外预测中何时利用伪相关

A common approach to out-of-distribution prediction restricts models to causal or invariant covariates to avoid spurious associations that may change across environments. Despite its theoretical appeal, this strategy can underperform empirical risk minimization when only a subset of the causal parents of the outcome is observed. In such settings, non-causal covariates can serve as proxies for unobserved causal parents and improve prediction when the proxy relationship is…

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Two-Sample IV: Efficient Two-Step Estimation and Tests for Overidentification and Weak-Instruments

两样本工具变量:有效两步估计、过度识别与弱工具检验

Two-sample IV is a popular estimation method when the outcome and treatment variables are available in different samples, whereas instruments are available in both samples. The standard estimator is two-sample two-stage least squares estimator, which is efficient under homoskedasticity and homogeneity of the samples. We develop a robust two-step procedure for efficient estimation under general heteroskedasticity and heterogeneity of the samples, and propose a related…

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Analysis of uncertain fixed-effects model for Latin square designs

拉丁方设计的不确定固定效应模型分析

Uncertain data without frequency stability often arises in experimental design. Classical fixed-effects models can only analyze precise experimental data. Based on an uncertain measure, this paper establishes uncertain fixed-effect models for Latin-square designs. First, we propose three methods with uncertainty to estimate the treatment and blocked effects and construct their confidence intervals. Then, uncertain homogeneity and common tests are conducted to assess the…

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