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Extended Fiducial Inference for Individual Treatment Effects via Deep Neural Networks

通过深度神经网络开展个体治疗效应的扩展信赖推断

Individual treatment effect estimation has gained significant attention in recent data science literature. This work introduces the Double Neural Network (Double-NN) method to address this problem within the framework of extended fiducial inference (EFI). In the proposed method, deep neural networks are used to model the treatment and control effect functions, while an additional neural network is employed to estimate their parameters. The universal approximation capability…

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Orthogonal Causal Calibration

正交因果校准

Estimates of heterogeneous treatment effects such as conditional average treatment effects (CATEs) and conditional quantile treatment effects (CQTEs) play an important role in real-world decision making. Given this importance, one should ensure these estimates are calibrated. While there is a rich literature on calibrating estimators of non-causal parameters, very few methods have been derived for calibrating estimators of causal parameters, or more generally estimators of…

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Policy Learning with Distributional Welfare

面向分布福利的政策学习

In this paper, we explore optimal treatment allocation policies that target distributional welfare. Most literature on treatment choice has considered utilitarian welfare based on the conditional average treatment effect (ATE). While average welfare is intuitive, it may yield undesirable allocations especially when individuals are heterogeneous (e.g., with outliers) - the very reason individualized treatments were introduced in the first place. This observation motivates us…

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Estimating treatment effects from observational data under truncation by death using survival-incorporated quantiles

死亡截断下利用纳入生存信息的分位数估计观测数据处理效应

The issue of "truncation by death" commonly arises in clinical research: subjects may die before their follow-up assessment, resulting in undefined clinical outcomes. To address this issue, we focus on survival-incorporated quantiles -- quantiles of a composite outcome combining death and clinical outcomes -- to summarize the effect of treatment. Using inverse probability of treatment weighting (IPTW), we propose an estimator for survival-incorporated quantiles from…

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Selective randomization inference for subgroup effects with continuous biomarkers

连续生物标志物亚组效应的选择性随机化推断

Randomization tests are a popular method for testing causal effects in clinical trials with finite-sample validity. In the presence of heterogeneous treatment effects, it is often of interest to select a subgroup that benefits from the treatment, frequently by choosing a cutoff for a continuous biomarker. However, selecting the cutoff and testing the effect on the same data may fail to control the type I error. To address this, we propose using "self-contained" methods for…

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A sliced Wasserstein and diffusion approach to random coefficient models

随机系数模型的切片 Wasserstein 距离与扩散方法

We propose a new minimum-distance estimator for linear random coefficient models. This estimator integrates the recently advanced sliced Wasserstein distance with the nearest neighbor methods, both of which enhance computational efficiency. We demonstrate that the proposed method is consistent in approximating the true distribution. Moreover, our formulation naturally leads to a diffusion process-based algorithm and is closely connected to treatment effect distribution…

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Estimation and Inference for the Average Treatment Effect in a Score-Explained Heterogeneous Treatment Effect Model

分数解释型异质处理效应模型中的平均处理效应估计与推断

In many practical situations, randomly assigning treatments to subjects is uncommon due to feasibility constraints. For example, economic aid programs and merit-based scholarships are often restricted to those meeting specific income or exam score thresholds. In these scenarios, traditional approaches to estimating treatment effects typically focus solely on observations near the cutoff point, thereby excluding a significant portion of the sample and potentially leading to…

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Inference with Many Weak Instruments and Heterogeneity

大量弱工具变量与处理效应异质性下的推断

This paper considers inference in a linear instrumental variable regression model with many potentially weak instruments, in the presence of heterogeneous treatment effects. I first show that existing test procedures, including those that are robust to either weak instruments or heterogeneous treatment effects, can be arbitrarily oversized. I propose a novel and valid test based on a score statistic and a ``leave-three-out" variance estimator. In the presence of…

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Dynamic Discrete-Continuous Choice Models: Identification and Conditional Choice Probability Estimation

动态离散与连续选择模型:识别与条件选择概率估计

This paper develops a general framework for dynamic models in which individuals simultaneously make both discrete and continuous choices. The framework incorporates a wide range of unobserved heterogeneity. I show that such models are nonparametrically identified. Based on constructive identification arguments, I build a novel two-step estimation method in the lineage of Hotz and Miller (1993) and Arcidiacono and Miller (2011) but extended to simultaneous discrete-continuous…

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Causal Inference for Genomic Data with Multiple Heterogeneous Outcomes

具有多个异质结局的基因组数据因果推断

With the evolution of single-cell RNA sequencing techniques into a standard approach in genomics, it has become possible to conduct cohort-level causal inferences based on single-cell-level measurements. However, the individual gene expression levels of interest are not directly observable; instead, only repeated proxy measurements from each individual's cells are available, providing a derived outcome to estimate the underlying outcome for each of many genes. In this paper,…

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Fused LASSO as Non-Crossing Quantile Regression

融合 LASSO 与非交叉分位数回归

Growth-at-Risk is vital for empirical macroeconomics but is often suspect to quantile crossing due to data limitations. While existing literature addresses this through post-processing of the fitted quantiles, these methods do not correct the estimated coefficients. We advocate for imposing non-crossing constraints during estimation and demonstrate their equivalence to fused LASSO with quantile-specific shrinkage parameters. By re-examining Growth-at-Risk through an…

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Bayesian analysis of regression discontinuity designs with heterogeneous treatment effects

异质处理效应断点回归设计的贝叶斯分析

Regression Discontinuity Design (RDD) is a popular framework for estimating a causal effect in settings where treatment is assigned if an observed covariate exceeds a fixed threshold. We consider estimation and inference in the common setting where the sample consists of multiple known sub-populations with potentially heterogeneous treatment effects. In the applied literature, it is common to account for heterogeneity by either fitting a parametric model or considering each…

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Conditional Inference for Secondary Outcomes Based on the Testing Result for the Primary Outcome in Clinical Trials

基于临床试验主要结局检验结果的次要结局条件推断

In clinical trials, inferences on clinical outcomes are often made conditional on specific selective processes. For instance, only when a treatment demonstrates a significant effect on the primary outcome, further analysis is conducted to investigate its efficacy on selected secondary outcomes. Similarly, inferences may also depend on whether a trial is terminated early at interim stage. While conventional approaches primarily aim to control the family-wise error rate…

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Deep Distributional Learning with Non-crossing Quantile Network

利用非交叉分位数网络进行深度分布学习

In this paper, we introduce a non-crossing quantile (NQ) network for conditional distribution learning. By leveraging non-negative activation functions, the NQ network ensures that the learned distributions remain monotonic, effectively addressing the issue of quantile crossing. Furthermore, the NQ network-based deep distributional learning framework is highly adaptable, applicable to a wide range of applications, from classical non-parametric quantile regression to more…

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Beyond Conditional Averages: Estimating The Individual Causal Effect Distribution

超越条件平均效应:估计个体因果效应分布

In recent years, the field of causal inference from observational data has emerged rapidly. The literature has focused on (conditional) average causal effect estimation. When (remaining) variability of individual causal effects (ICEs) is considerable, average effects may be uninformative for an individual. The fundamental problem of causal inference precludes estimating the joint distribution of potential outcomes without making assumptions. In this work, we show that the…

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Forecasting a time series of Lorenz curves: One-way functional analysis of variance

洛伦兹曲线时间序列预测:单因素函数型方差分析

The Lorenz curve is a fundamental tool for analysing income and wealth distribution and inequality at national and regional levels. We utilise a one-way functional analysis of variance to decompose a time series of Lorenz curves and develop a method for producing one-step-ahead point and interval forecasts. The one-way functional analysis of variance is easily interpretable by decomposing an array into a functional grand effect, a functional row effect and residual…

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Regression Discontinuity Design with Distribution-Valued Outcomes

分布值结局的断点回归设计

This article introduces Regression Discontinuity Design (RDD) with Distribution-Valued Outcomes (R3D), extending the standard RDD framework to settings where the outcome is a distribution rather than a scalar. Such settings arise when treatment is assigned at a higher level of aggregation than the outcome-for example, when a subsidy is allocated based on a firm-level revenue cutoff while the outcome of interest is the distribution of employee wages within the firm. Since…

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Non-parametric Quantile Regression and Uniform Inference with Unknown Error Distribution

未知测量误差分布下的非参数分位数回归与一致推断

This paper studies the non-parametric estimation and uniform inference for the conditional quantile regression function (CQRF) with covariates exposed to measurement errors. We consider the case that the distribution of the measurement error is unknown and allowed to be either ordinary or super smooth. We estimate the density of the measurement error by the repeated measurements and propose the deconvolution kernel estimator for the CQRF. We derive the uniform Bahadur…

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Dependence-based fuzzy clustering of functional time series

基于依赖结构的函数型时间序列模糊聚类

Time series clustering is essential in scientific applications, yet methods for functional time series, collections of infinite-dimensional curves treated as random elements in a Hilbert space, remain underdeveloped. This work presents clustering approaches for functional time series that combine the fuzzy $C$-medoids and fuzzy $C$-means procedures with a novel dissimilarity measure tailored for functional data. This dissimilarity is based on an extension of the quantile…

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Non-parametric cure models through extreme-value tail estimation

基于极值尾部估计的非参数治愈模型

In survival analysis, the estimation of the proportion of subjects who will never experience the event of interest, termed the cure rate, has received considerable attention recently. Its estimation can be a particularly difficult task when follow-up is not sufficient, that is when the censoring mechanism has a smaller support than the distribution of the target data. In the latter case, non-parametric estimators were recently proposed using extreme value methodology,…

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A Unified Approach for Estimating Various Treatment Effects in Causal Inference

因果推断中多类处理效应的统一估计方法

In this paper, we introduce a unified estimator to analyze various treatment effects in causal inference, including but not limited to the average treatment effect (ATE) and the quantile treatment effect (QTE). The proposed estimator is developed under the statistical functional and cumulative distribution function structure, which leads to a flexible and robust estimator and covers some frequent treatment effects. In addition, our approach also takes variable selection into…

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Bounds on the Distribution of a Sum of Two Random Variables: Revisiting a problem of Kolmogorov with application to Individual Treatment Effects

两个随机变量之和的分布界:重访Kolmogorov问题及个体处理效应应用

We revisit the following problem, proposed by Kolmogorov: given prescribed marginal distributions $F$ and $G$ for random variables $X,Y$ respectively, characterize the set of compatible distribution functions for the sum $Z=X+Y$. Bounds on the distribution function for $Z$ were first given by Markarov (1982) and Rüschendorf (1982) independently. Frank et al. (1987) provided a solution to the same problem using copula theory. However, though these authors obtain the same…

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Minimax Rate-Optimal Inference for Individualized Quantile Treatment Effects in High-dimensional Models

高维模型中个体化分位数处理效应的极小极大速率最优推断

The quantification of treatment effects plays an important role in a wide range of applications, including policy making and bio-pharmaceutical research. In this article, we study the quantile treatment effect (QTE) while addressing two specific types of heterogeneities: (a) personalized heterogeneity, which captures the varying treatment effects for different individuals, and (b) quantile heterogeneity, which accounts for how the impact of covariates varies across different…

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Integrative Analysis of High-dimensional RCT and RWD Subject to Censoring and Hidden Confounding

删失与隐藏混杂下高维随机试验和真实世界数据的整合分析

In this study, we focus on estimating the heterogeneous treatment effect (HTE) for survival outcome. The outcome is subject to censoring and the number of covariates is high-dimensional. We utilize data from both the randomized controlled trial (RCT), considered as the gold standard, and real-world data (RWD), possibly affected by hidden confounding factors. To achieve a more efficient HTE estimate, such integrative analysis requires great insight into the data generation…

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