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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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SCOPE Shrinkage: A Unified Framework for Wavelet Denoising

SCOPE 收缩:小波去噪的统一框架

We introduce Symmetric CDF Oriented Probability Enhanced (SCOPE) shrinkage, a unified family of sign-preserving shrinkage rules constructed from centered cumulative distribution functions of symmetric unimodal distributions. The proposed framework generates a broad class of attenuation profiles that interpolate between strong local shrinkage near zero and asymptotically unbiased behavior in the tails. A general formulation is developed that separates scale and shape effects…

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Was Javert right to be suspicious? Marginal Treatment Effects with Duration Outcomes

冉阿让的警探有理由怀疑吗?持续时间结果的边际处理效应

We identify the distributional and quantile marginal treatment effect functions when the outcome is right-censored. Our method requires a conditionally exogenous instrument and random censoring. We propose asymptotically consistent semi-parametric estimators and valid inferential procedures for the target functions. To illustrate, we evaluate the effect of alternative sentences (fines and community service vs. no punishment) on recidivism in Brazil. Our results highlight…

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Wasserstein Policy Learning for Distributional Outcomes

分布型结局的 Wasserstein 政策学习

Offline policy learning has received growing attention in causal inference. The primary objective is to learn a policy (individualized treatment rule) as a mapping from covariates to treatment that maximizes the empirical welfare defined as the mean of scalar-valued potential outcomes. In this paper, we study offline policy learning with distribution-valued outcomes, where each potential outcome is a probability measure on $\mathbb{R}$ and the reward is defined through a…

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Distributional Instrumental Variable Method

分布工具变量方法

The instrumental variable (IV) approach is commonly used to infer causal effects in the presence of unmeasured confounding. Existing methods typically aim to estimate the mean causal effects, whereas a few other methods focus on quantile treatment effects. The aim of this work is to estimate the entire interventional distribution. We propose a method called Distributional Instrumental Variable (DIV), which uses generative modelling in a nonlinear IV setting. We establish…

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Correcting Sample Selection Bias in PISA Rankings

校正 PISA 排名中的样本选择偏差

This paper proposes a method to account for sample selection (survivor bias) in cross-country comparisons. International assessments such as the Programme for International Student Assessment (PISA) observe outcomes only for students enrolled in school at age 15, which can distort comparisons in countries with high dropout rates. I consider a quantile-based selection correction that delivers bounds on countries' average performance rather than point estimates. Using these…

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Panel Quantile Regression with Common Shocks

共同冲击下的面板分位数回归

This paper develops an asymptotic and inferential theory for fixed-effects panel quantile regression (FEQR) that delivers inference robust to pervasive common shocks. Such shocks induce cross-sectional dependence that is central in many economic and financial panels but largely ignored in existing FEQR theory, which typically assumes cross-sectional independence and requires $T \gg N$. We show that the standard FEQR estimator remains asymptotically normal under the mild…

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Bounding Causal Effects for Ordinal Outcomes Under Positive Dependence

正依赖条件下有序结果因果效应的界限

Defining and estimating causal effects for ordinal data is challenging. Standard average treatment effects are not appropriate for ordinal scales, and alternative estimands, such as the probabilities that the treatment outcome exceeds or does not worsen the control outcome, are generally not identifiable. Existing work provides sharp bounds for these quantities based only on marginal distributions. Motivated by a previous observation showing that bounds obtained under an…

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Decision Theory for the Archetype Discovery Problem

原型发现问题的决策理论

In the archetype discovery problem a researcher wants to summarize N heterogeneous policy effects of interest that vary over a discrete set of covariates. The goal is to partition the set of covariates into K<N groups -- the archetype sets -- and to provide a summary of the policy effects for each group. We use decision theory to show that, under a weighted mean-squared-error criterion, a procedure analogous to the Sorted Group Average Treatment Effects (GATES) solves the…

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Bayesian Penalized Transformation Models: Structured Additive Location-Scale Regression for Arbitrary Conditional Distributions

贝叶斯惩罚变换模型:面向任意条件分布的结构化可加位置—尺度回归

Penalized transformation models (PTMs) are a semiparametric location-scale regression family that estimate a response's conditional distribution directly from the data, and model the location and scale through structured additive predictors. The core of the model is a monotonically increasing transformation function that relates the response distribution to a reference distribution. The transformation function is equipped with a smoothness prior that regularizes how much the…

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Estimation and Inference for the $τ$-Quantile of Individual Heterogeneous Coefficient

个体异质系数 τ 分位数的估计与推断

This paper proposes estimation and inference procedures for quantiles of the heterogeneous individual-specific coefficients in panel data. Unlike conventional panel quantile regression, which focuses on outcome heterogeneity, our approach targets the $τ$-quantile of the cross-sectional distribution of individual-specific slopes. We establish the asymptotic theory under both stochastic and deterministic designs, with convergence rates $\sqrt{N}$ and $\sqrt{N\sqrt{T}}$,…

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A Synthetic Control Approach to Conditional Distributional Treatment Effects

条件分布处理效应的合成控制方法

This paper proposes a synthetic control (SC) framework for the estimation of conditional distributional treatment effects. Identification rests on a parallel trends condition formulated in the parameter space of the semiparametric distribution regression (DR) model, which keeps the counterfactual conditional distribution within the model class. The weights solve a least-squares problem subject to an adding-up constraint, yielding a closed-form estimator. We derive the…

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Model Risk in Machine-Learning Distributional IV Estimation

机器学习分布型工具变量估计中的模型风险

We study model risk in machine-learning estimation of the Distributional Instrumental Variable Local Average Treatment Effect (D-IV-LATE), the distributional IV effect for the subpopulation induced into treatment by the instrument. The contribution is not a new neural causal estimand. We implement a reduced-form orthogonal level-score DML estimator for the covariate-adjusted D-IV-LATE target and use it to ask how much the nuisance learner matters for distributional IV…

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Treatment Allocation under Uncertain Costs

成本不确定时的处理分配

We consider the problem of learning how to optimally allocate treatments whose cost is uncertain and can vary with pre-treatment covariates. This setting may arise in medicine if we need to prioritize access to a scarce resource that different patients would use for different amounts of time, or in marketing if we want to target discounts whose cost to the company depends on how much the discounts are used. Here, we show that the optimal treatment allocation rule under…

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Synthesizing Evidence: Data-Pooling as a Tool for Treatment Selection in Online Experiments

综合证据:利用在线实验数据汇集选择处理方案

Randomized experiments are the gold standard for causal inference but face significant challenges in business applications, including limited traffic allocation, the need for heterogeneous treatment effect estimation, and the complexity of managing overlapping experiments. These factors lead to high variability in treatment effect estimates, making data-driven policy roll out difficult. To address these issues, we introduce the data pooling treatment roll-out (DPTR)…

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Beyond Means: Topological Causal Effects under Persistent-Homology Ignorability

超越均值:持久同调可忽略性下的拓扑因果效应

Average treatment effects (ATE) and conditional average treatment effects (CATE) are foundational causal estimands, but they target changes in expected outcomes and can miss treatment-induced changes in the shape of outcome distributions. A canonical failure mode occurs when control outcomes are unimodal, treated outcomes become bimodal, and both distributions have the same mean. In such cases mean-based causal estimands are zero even though the geometry and topology of the…

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Topological Ignorability for Structural Causal Effects Beyond Means

超越均值的结构性因果效应与拓扑可忽略性

Many interventions alter the structure of an outcome distribution rather than its mean: they can split a population into disconnected regimes, create loops or holes, generate branches, or reorganize an outcome cloud while leaving the average response nearly unchanged. In such settings, mean-based causal estimands such as the average treatment effect may miss important structural effects. We introduce topological-geometrical causal metrics based on summaries of interventional…

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Distributional Effects with Two-Sided Measurement Error: An Application to Intergenerational Income Mobility

双侧测量误差下的分布效应:代际收入流动应用

This paper considers identification and estimation of distributional effect parameters that depend on the joint distribution of an outcome and another variable of interest ("treatment") in a setting with "two-sided" measurement error -- that is, where both variables are possibly measured with error. Examples of these parameters in the context of intergenerational income mobility include transition matrices, rank-rank correlations, and the poverty rate of children as a…

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Random Set Quantile Estimation of Partially Identified Discrete Response Models

部分识别离散响应模型的随机集分位数估计

Semiparametric discrete choice models are widely applied in economics, yet a fundamental tension arises when covariates are discrete as regression coefficients that are point identified under continuous regressors may become only partially identified. We show that this is not merely an identification problem but creates serious estimation pathologies. Classical estimators, including the maximum score estimator of Manski (1975), not only have population maximizers that are…

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Hypothesis Testing for a Functional Parameter via Self-normalization

通过自归一化检验函数型参数的假设

Testing simple or composite hypothesis on a functional parameter has attracted considerable attention in time series analysis. To accommodate for the unknown temporal dependence, classical nonparametric approaches such as block bootstrapping and subsampling all involve a bandwidth parameter, the choice of which can substantially affect the finite sample performance. The self normalization (SN) method is tuning parameter free when applied to the inference of a…

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Improved Guarantees for Heterogeneous Treatment-Effect Estimation via Matrix Completion

通过矩阵补全改进异质性处理效应估计的理论保证

A central goal of modern causal inference is estimating heterogeneous treatment effects to answer questions like "how does an intervention affect each unit," rather than only on average. We study this problem with panel-data where we observe $n$ units across $m$ times under unknown, non-uniform treatment assignments. The data in this setting is naturally represented as a matrix of all unit--time treatment effects. Estimating heterogeneous treatment effects can then be…

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IV regression with distribution-valued outcomes

分布值结局的工具变量回归

We develop IV Fréchet regression (IVFR), an instrumental-variable (IV) method for settings where the outcome is an entire distribution. Framing the problem as an IV regression in 2-Wasserstein space, IVFR extends global Fréchet regression to the case with endogenous covariates. IVFR projects IV-weighted quantile curves onto the space of valid distributions and then recovers the corresponding regression coefficient functions. The projection provably reduces the estimation…

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Learning a directed acyclic graph with additive heteroscedastic errors

具有加性异方差误差的有向无环图学习

This paper studies causal discovery for a directed acyclic graph under a structural equation model with additive heteroscedastic errors. We first establish new identifiability results for location-scale noise models, showing that heteroscedasticity can be leveraged to recover causal directions. Based on these insights, we propose a novel iterative procedure, Residual Simultaneous Quantile Estimation (RESQUE), where each iteration consists of a residual-construction stage and…

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Joint Estimation of Marginal and Heterogeneous Treatment Effects

边际处理效应与异质性处理效应的联合估计

Randomized clinical trials typically aim to estimate a marginal treatment effect. While covariate adjustment can improve precision, it may change the estimand in nonlinear models due to noncollapsibility, leading to conditional rather than marginal treatment effects. At the same time, identifying prognostic and predictive covariates is important for understanding treatment effect heterogeneity and informing clinical decision-making. Keeping marginal interpretability while…

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