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Optimal Estimation Methodologies for Panel Data Regression Models

面板数据回归模型的最优估计方法综述

This survey study discusses main aspects to optimal estimation methodologies for panel data regression models. In particular, we present current methodological developments for modeling stationary panel data as well as robust methods for estimation and inference in nonstationary panel data regression models. Some applications from the network econometrics and high dimensional statistics literature are also discussed within a stationary time series environment.

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Asymptotic in a class of network models with an increasing sub-Gamma degree sequence

次伽马噪声度序列下网络模型的渐近性质

For the differential privacy under the sub-Gamma noise, we derive the asymptotic properties of a class of network models with binary values with a general link function. In this paper, we release the degree sequences of the binary networks under a general noisy mechanism with the discrete Laplace mechanism as a special case. We establish the asymptotic result including both consistency and asymptotically normality of the parameter estimator when the number of parameters goes…

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Covariate-adaptive randomization inference in matched designs

匹配设计中的协变量自适应随机化推断

It is common to conduct causal inference in matched observational studies by proceeding as though treatment assignments within matched sets are assigned uniformly at random and using this distribution as the basis for inference. This approach ignores observed discrepancies in matched sets that may be consequential for the distribution of treatment, which are succinctly captured by within-set differences in the propensity score. We address this problem via covariate-adaptive…

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Causal inference with a functional outcome

函数型结果的因果推断

This paper presents methods to study the causal effect of a binary treatment on a functional outcome with observational data. We define a Functional Average Treatment Effect and develop an outcome regression estimator. We show how to obtain valid inference on the FATE using simultaneous confidence bands, which cover the FATE with a given probability over the entire domain. Simulation experiments illustrate how the simultaneous confidence bands take the multiple comparison…

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Semiparametric Discrete Choice Models for Bundles

商品组合选择的半参数离散选择模型

We propose two approaches to estimate semiparametric discrete choice models for bundles. Our first approach is a kernel-weighted rank estimator based on a matching-based identification strategy. We establish its complete asymptotic properties and prove the validity of the nonparametric bootstrap for inference. We then introduce a new multi-index least absolute deviations (LAD) estimator as an alternative, of which the main advantage is its capacity to estimate preference…

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CausalImages: An R Package for Causal Inference with Earth Observation, Bio-medical, and Social Science Images

CausalImages:面向地球观测、生物医学与社会科学图像的因果推断 R 包

The causalimages R package enables causal inference with image and image sequence data, providing new tools for integrating novel data sources like satellite and bio-medical imagery into the study of cause and effect. One set of functions enables image-based causal inference analyses. For example, one key function decomposes treatment effect heterogeneity by images using an interpretable Bayesian framework. This allows for determining which types of images or image sequences…

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Estimating Causal Effects with Hidden Confounding using Instrumental Variables and Environments

利用工具变量与环境估计存在隐藏混杂的因果效应

Recent works have proposed regression models which are invariant across data collection environments. These estimators often have a causal interpretation under conditions on the environments and type of invariance imposed. One recent example, the Causal Dantzig (CD), is consistent under hidden confounding and represents an alternative to classical instrumental variable estimators such as Two Stage Least Squares (TSLS). In this work we derive the CD as a generalized method of…

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Counterfactually Comparing Abstaining Classifiers

以反事实方式比较可拒绝预测的分类器

Abstaining classifiers have the option to abstain from making predictions on inputs that they are unsure about. These classifiers are becoming increasingly popular in high-stakes decision-making problems, as they can withhold uncertain predictions to improve their reliability and safety. When evaluating black-box abstaining classifier(s), however, we lack a principled approach that accounts for what the classifier would have predicted on its abstentions. These missing…

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Identifiability Guarantees for Causal Disentanglement from Soft Interventions

软干预下因果解耦的可识别性保证

Causal disentanglement aims to uncover a representation of data using latent variables that are interrelated through a causal model. Such a representation is identifiable if the latent model that explains the data is unique. In this paper, we focus on the scenario where unpaired observational and interventional data are available, with each intervention changing the mechanism of a latent variable. When the causal variables are fully observed, statistically consistent…

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Long-Term Causal Inference with Imperfect Surrogates using Many Weak Experiments, Proxies, and Cross-Fold Moments

不完美替代指标下的长期因果推断:众多弱实验、代理与跨折矩

Inferring causal effects on long-term outcomes using short-term surrogates is crucial to rapid innovation. However, even when treatments are randomized and surrogates fully mediate their effect on outcomes, it's possible that we get the direction of causal effects wrong due to confounding between surrogates and outcomes -- a situation famously known as the surrogate paradox. The availability of many historical experiments offer the opportunity to instrument for the surrogate…

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Learned Causal Method Prediction

通过学习预测适用的因果方法

For a given causal question, it is important to efficiently decide which causal inference method to use for a given dataset. This is challenging because causal methods typically rely on complex and difficult-to-verify assumptions, and cross-validation is not applicable since ground truth causal quantities are unobserved. In this work, we propose CAusal Method Predictor (CAMP), a framework for predicting the best method for a given dataset. To this end, we generate datasets…

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Flexibly Estimating and Interpreting Heterogeneous Treatment Effects of Laparoscopic Surgery for Cholecystitis Patients

灵活估计与解释胆囊炎患者腹腔镜手术的异质性治疗效应

Laparoscopic surgery has been shown through a number of randomized trials to be an effective form of treatment for cholecystitis. Given this evidence, one natural question for clinical practice is: does the effectiveness of laparoscopic surgery vary among patients? It might be the case that, while the overall effect is positive, some patients treated with laparoscopic surgery may respond positively to the intervention while others do not or may be harmed. In our study, we…

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How Much Should We Trust Instrumental Variable Estimates in Political Science? Practical Advice Based on Over 60 Replicated Studies

政治学中的工具变量估计有多可信?基于六十余项复现的实践建议

Instrumental variable (IV) strategies are widely used in political science to establish causal relationships. However, the identifying assumptions required by an IV design are demanding, and it remains challenging for researchers to assess their validity. In this paper, we replicate 67 papers published in three top journals in political science during 2010-2022 and identify several troubling patterns. First, researchers often overestimate the strength of their IVs due to…

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Asymmetric predictability in causal discovery: an information theoretic approach

因果发现中的预测不对称性:信息论方法

Causal investigations in observational studies pose a great challenge in research where randomized trials or intervention-based studies are not feasible. We develop an information geometric causal discovery and inference framework of "predictive asymmetry". For $(X, Y)$, predictive asymmetry enables assessment of whether $X$ is more likely to cause $Y$ or vice-versa. The asymmetry between cause and effect becomes particularly simple if $X$ and $Y$ are deterministically…

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Asymptotic Properties of Endogeneity Corrections Using Nonlinear Transformations

利用非线性变换修正内生性的渐近性质

This paper considers a linear regression model with an endogenous regressor which arises from a nonlinear transformation of a latent variable. It is shown that the corresponding coefficient can be consistently estimated without external instruments by adding a rank-based transformation of the regressor to the model and performing standard OLS estimation. In contrast to other approaches, our nonparametric control function approach does not rely on a conformably specified…

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Debiased Fixed Effects Estimation of Binary Logit Models with Three-Dimensional Panel Data

三维面板二元 Logit 模型的去偏固定效应估计

Naive maximum likelihood estimation of binary logit models with fixed effects leads to unreliable inference due to the incidental parameter problem. We study the case of three-dimensional panel data, where the model includes three sets of additive and overlapping unobserved effects. This encompasses models for network panel data, where senders and receivers maintain bilateral relationships over time, and fixed effects account for unobserved heterogeneity at the sender-time,…

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Exposure Effects on Count Outcomes with Observational Data, with Application to Incarcerated Women

观察数据中暴露对计数结果的效应:以被监禁女性为例

Causal inference methods can be applied to estimate the effect of a point exposure or treatment on an outcome of interest using data from observational studies. For example, in the Women's Interagency HIV Study, it is of interest to understand the effects of incarceration on the number of sexual partners and the number of cigarettes smoked after incarceration. In settings like this where the outcome is a count, the estimand is often the causal mean ratio, i.e., the ratio of…

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A Ridge-Regularised Jackknifed Anderson-Rubin Test

岭正则化的刀切 Anderson–Rubin 检验

We consider hypothesis testing in instrumental variable regression models with few included exogenous covariates but many instruments -- possibly more than the number of observations. We show that a ridge-regularised version of the jackknifed Anderson Rubin (1949, henceforth AR) test controls asymptotic size in the presence of heteroskedasticity, and when the instruments may be arbitrarily weak. Asymptotic size control is established under weaker assumptions than those…

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Graphical tools for selecting conditional instrumental sets

选择条件工具变量集合的图形工具

We consider the efficient estimation of total causal effects in the presence of unmeasured confounding using conditional instrumental sets. Specifically, we consider the two-stage least squares estimator in the setting of a linear structural equation model with correlated errors that is compatible with a known acyclic directed mixed graph. To set the stage for our results, we characterize the class of linearly valid conditional instrumental sets that yield consistent…

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Optimal Treatment Allocation for Efficient Policy Evaluation in Sequential Decision Making

序贯决策中用于高效政策评估的最优处理分配

A/B testing is critical for modern technological companies to evaluate the effectiveness of newly developed products against standard baselines. This paper studies optimal designs that aim to maximize the amount of information obtained from online experiments to estimate treatment effects accurately. We propose three optimal allocation strategies in a dynamic setting where treatments are sequentially assigned over time. These strategies are designed to minimize the variance…

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Identification of time-varying counterfactual parameters in nonlinear panel models

非线性面板模型中时变反事实参数的识别

We develop a general framework for the identification of counterfactual parameters in a class of nonlinear semiparametric panel models with fixed effects and time effects. Our method applies to models for discrete outcomes (e.g., two-way fixed effects binary choice) or continuous outcomes (e.g., censored regression), with discrete or continuous regressors. Our results do not require parametric assumptions on the error terms or time-homogeneity on the outcome equation. Our…

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Detecting hidden confounding in observational data using multiple environments

利用多个环境的观测数据检测隐藏混杂

A common assumption in causal inference from observational data is that there is no hidden confounding. Yet it is, in general, impossible to verify this assumption from a single dataset. Under the assumption of independent causal mechanisms underlying the data-generating process, we demonstrate a way to detect unobserved confounders when having multiple observational datasets coming from different environments. We present a theory for testable conditional independencies that…

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High Precision Causal Model Evaluation with Conditional Randomization

条件随机化下的高精度因果模型评估

The gold standard for causal model evaluation involves comparing model predictions with true effects estimated from randomized controlled trials (RCT). However, RCTs are not always feasible or ethical to perform. In contrast, conditionally randomized experiments based on inverse probability weighting (IPW) offer a more realistic approach but may suffer from high estimation variance. To tackle this challenge and enhance causal model evaluation in real-world conditional…

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The use of restricted mean survival time to estimate treatment effect under model misspecification, a simulation study

模型误设下利用限制平均生存时间估计治疗效应:模拟研究

The use of the non-parametric Restricted Mean Survival Time endpoint (RMST) has grown in popularity as trialists look to analyse time-to-event outcomes without the restrictions of the proportional hazards assumption. In this paper, we evaluate the power and type I error rate of the parametric and non-parametric RMST estimators when treatment effect is explained by multiple covariates, including an interaction term. Utilising the RMST estimator in this way allows the combined…

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