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Design-Based Uncertainty for Quasi-Experiments

准实验的设计型不确定性

Design-based frameworks of uncertainty are frequently used in settings where the treatment is (conditionally) randomly assigned. This paper develops a design-based framework suitable for analyzing quasi-experimental settings in the social sciences, in which the treatment assignment can be viewed as the realization of some stochastic process but there is concern about unobserved selection into treatment. In our framework, treatments are stochastic, but units may differ in…

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Evaluating Program Sequences with Double Machine Learning: An Application to Labor Market Policies

用双重机器学习评估项目序列:劳动力市场政策应用

Many programs evaluated in observational studies incorporate a sequential structure, where individuals may be assigned to various programs over time. While this complexity is often simplified by analyzing programs at single points in time, this paper reviews, explains, and applies methods for program evaluation within a sequential framework. It outlines the assumptions required for identification under dynamic confounding and demonstrates how extending sequential estimands…

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Modeling Complex Life Systems: Bayesian Inference for Weibull Failure Times Using Adaptive MCMC

复杂生命系统的 Weibull 失效时间建模:自适应 MCMC 贝叶斯推断

This research develops a Bayesian framework for analyzing failure times using the Weibull distribution, addressing challenges in prior selection due to the lack of conjugate priors and multi-dimensional sufficient statistics. We propose an adaptive semi-parametric MCMC algorithm for lifetime data analysis, employing a hierarchical Bayesian model and the No-U-Turn Sampler (NUTS) in STAN. Twenty-four combinations of prior distributions are evaluated, with a noninformative…

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Covariance matrix estimation in the singular case using regularized Cholesky factor

奇异情形下基于正则化 Cholesky 因子的协方差矩阵估计

We consider estimating the population covariance matrix when the number of available samples is less than the size of the observations. The sample covariance matrix (SCM) being singular, regularization is mandatory in this case. For this purpose we consider minimizing Stein's loss function and we investigate a method based on augmenting the partial Cholesky decomposition of the SCM. We first derive the finite sample optimum estimator which minimizes the loss for each data…

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Let the Tree Decide: FABART A Non-Parametric Factor Model

让树模型决定:非参数因子模型 FABART

This article proposes a novel framework that integrates Bayesian Additive Regression Trees (BART) into a Factor-Augmented Vector Autoregressive (FAVAR) model to forecast macro-financial variables and examine asymmetries in the transmission of oil price shocks. By employing nonparametric techniques for dimension reduction, the model captures complex, nonlinear relationships between observables and latent factors that are often missed by linear approaches. A simulation…

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Berry-Esseen bounds for design-based causal inference with possibly diverging treatment levels and varying group sizes

处理水平可增长且组规模不同时设计型因果推断的 Berry–Esseen 界

Neyman (1923/1990) introduced the randomization model, which contains the notation of potential outcomes to define causal effects and a framework for large-sample inference based on the design of the experiment. However, the existing theory for this framework is far from complete, especially when the number of treatment levels diverges and the treatment group sizes vary. We provide a unified discussion of statistical inference under the randomization model with general…

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Bayesian Sensitivity Analysis for Causal Estimation with Time-varying Unmeasured Confounding

时变未测量混杂下因果估计的贝叶斯敏感性分析

Causal inference relies on the untestable assumption of no unmeasured confounding. Sensitivity analysis can be used to quantify the impact of unmeasured confounding on causal estimates. Among sensitivity analysis methods proposed in the literature for unmeasured confounding, the latent confounder approach is favoured for its intuitive interpretation via the use of bias parameters to specify the relationship between the observed and unobserved variables and the sensitivity…

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Variance estimation after matching or re-weighting

匹配或重新加权后的方差估计

This paper develops a variance estimation framework for matching estimators that enables valid population inference for treatment effects. We provide theoretical analysis of a variance estimator that addresses key limitations in the existing literature. While Abadie and Imbens (2006) proposed a foundational variance estimator requiring matching for both treatment and control groups, this approach is computationally prohibitive and rarely used in practice. Our method provides…

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Nonparametric estimation of an optimal treatment rule with fused randomized trials and missing effect modifiers

融合随机试验且效应修饰变量缺失时最优治疗规则的非参数估计

A fundamental principle of clinical medicine is that a treatment should only be administered to those patients who would benefit from it. Treatment strategies that assign treatment to patients as a function of their individual characteristics are known as dynamic treatment rules. The dynamic treatment rule that optimizes the outcome in the population is called the optimal dynamic treatment rule. Randomized clinical trials are considered the gold standard for estimating the…

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Testing Generalizability in Causal Inference

因果推断中的泛化能力检验

Ensuring robust model performance in diverse real-world scenarios requires addressing generalizability across domains with covariate shifts. However, no formal procedure exists for statistically evaluating generalizability in machine learning algorithms. Existing predictive metrics like mean squared error (MSE) help to quantify the relative performance between models, but do not directly answer whether a model can or cannot generalize. To address this gap in the domain of…

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Inference on panel data models with a generalized factor structure

广义因子结构面板模型的统计推断

We consider identification, inference and validation of linear panel data models when both factors and factor loadings are accounted for by a nonparametric function. This general specification encompasses rather popular models such as the two-way fixed effects and the interactive fixed effects ones. By applying a conditional mean independence assumption between unobserved heterogeneity and the covariates, we obtain consistent estimators of the parameters of interest at the…

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Are you doing better than random guessing? A call for using negative controls when evaluating causal discovery algorithms

因果发现优于随机猜测吗?评估算法时使用负对照

New proposals for causal discovery algorithms are typically evaluated using simulations and a few selected real data examples with known data generating mechanisms. However, there does not exist a general guideline for how such evaluation studies should be designed, and therefore, comparing results across different studies can be difficult. In this article, we propose to use negative controls as a common evaluation baseline by posing the question: Are we doing better than…

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Sharp Bounds for Continuous-Valued Treatment Effects with Unobserved Confounders

存在未观测混杂时连续处理效应的锐界

In causal inference, treatment effects are typically estimated under the ignorability, or unconfoundedness, assumption, which is often unrealistic in observational data. By relaxing this assumption and conducting a sensitivity analysis, we introduce novel bounds and derive confidence intervals for the Average Potential Outcome (APO) - a standard metric for evaluating continuous-valued treatment or exposure effects. We demonstrate that these bounds are sharp under a…

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A note on the properties of the confidence set for the local average treatment effect obtained by inverting the score test

反演得分检验得到的局部平均处理效应置信集性质

We study the properties of the score confidence set for the local average treatment effect in non and semiparametric instrumental variable models. This confidence set is constructed by inverting a score test based on an estimate of the nonparametric influence function for the estimand, and is known to be uniformly valid in models that allow for arbitrarily weak instruments; because of this, the confidence set can have infinite diameter at some laws. We characterize the six…

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Conditional Triple Difference-in-Differences

条件三重差分法

Triple difference-in-differences designs are widely used to estimate causal effects in empirical work. Surveying the literature, we find that most applications include controls. We show that this standard practice is generally biased for the target causal estimand when covariate distributions differ across groups. To address this, we propose identifying a causal estimand by fixing the covariate distribution to that of one group. We then develop a double-robust estimator and…

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Efficiency of QMLE for dynamic panel data models with interactive effects

含交互效应动态面板模型的准极大似然估计效率

This paper studies the problem of efficient estimation of panel data models in the presence of an increasing number of incidental parameters. We formulate the dynamic panel as a simultaneous equations system, and derive the efficiency bound under the normality assumption. We then show that the Gaussian quasi-maximum likelihood estimator (QMLE) applied to the system achieves the normality efficiency bound without the normality assumption. Comparison of QMLE with the fixed…

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Almost-Optimal Local-Search Methods for Sparse Tensor PCA

稀疏张量PCA的近乎最优局部搜索方法

Local-search methods are widely employed in statistical applications, yet interestingly, their theoretical foundations remain rather underexplored, compared to other classes of estimators such as low-degree polynomials and spectral methods. Of note, among the few existing results recent studies have revealed a significant "local-computational" gap in the context of a well-studied sparse tensor principal component analysis (PCA), where a broad class of local Markov chain…

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Estimating the Number of Components in Panel Data Finite Mixture Regression Models with an Application to Production Function Heterogeneity

面板有限混合回归的成分数估计及生产函数异质性应用

This paper develops statistical methods for determining the number of components in panel data finite mixture regression models with regression errors independently distributed as normal or more flexible normal mixtures. We analyze the asymptotic properties of the likelihood ratio test (LRT) and information criteria (AIC and BIC) for model selection in both conditionally independent and dynamic panel settings. Unlike cross-sectional normal mixture models, we show that panel…

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Causal effects on non-terminal event time with application to antibiotic usage and future resistance

非终末事件时间的因果效应:抗生素使用与未来耐药性

Comparing future antibiotic resistance levels resulting from different antibiotic treatments is challenging because some patients may survive only under one of the antibiotic treatments. We embed this problem within a semi-competing risks approach to study the causal effect on resistant infection, treated as a non-terminal event time. We argue that existing principal stratification estimands for such problems exclude patients for whom a causal effect is well-defined and is…

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Diffusion index forecasts under weaker loadings: PCA, ridge regression, and random projections

较弱载荷下的扩散指数预测:主成分、岭回归与随机投影

We study the accuracy of forecasts in the diffusion index forecast model with possibly weak loadings. The default option to construct forecasts is to estimate the factors through principal component analysis (PCA) on the available predictor matrix, and use the estimated factors to forecast the outcome variable. Alternatively, we can directly relate the outcome variable to the predictors through either ridge regression or random projections. We establish that forecasts based…

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Statistical Inference for Cumulative INAR($\infty$) Processes via Least-Squares

累计无限阶整数值自回归过程的最小二乘统计推断

This paper investigates the cumulative Integer-Valued Autoregressive model of infinite order, denoted as INAR($\infty$), a class of processes crucial for modeling count time series and equivalent to discrete-time Hawkes processes. We propose a computationally efficient conditional least-squares (CLS) estimator to address the challenge of parameter inference in this infinite-dimensional setting. We establish the key theoretical properties of the estimator, including its…

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Functional Tensor Regression

函数型张量回归

Tensor regression has attracted significant attention in statistical research. This study tackles the challenge of handling covariates with smooth varying structures. We introduce a novel framework, termed functional tensor regression, which incorporates both the tensor and functional aspects of the covariate. To address the high dimensionality and functional continuity of the regression coefficient, we employ a low Tucker rank decomposition along with smooth regularization…

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Fisher's Randomization Test for Causality with General Types of Treatments

适用于一般处理类型的 Fisher 因果随机化检验

We extend Fisher's randomization test (FRT) to test conditional independence between observed outcomes and treatments given covariates in both randomized experiments and observational studies, with no restriction on the variable type of treatments. Under a generalized unconfoundedness assumption, we provide causal identification for this hypothesis. Our approach requires neither the no-interference nor the positive overlap assumption, making it a widely applicable tool for…

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Longitudinal weighted and trimmed treatment effects with flip interventions

基于翻转干预的纵向加权与修剪处理效应

Weighting and trimming are popular methods for addressing positivity violations in causal inference. While well-studied with single-timepoint data, standard methods do not easily generalize to address non-baseline positivity violations in longitudinal data, and remain vulnerable to such violations. In this paper, we extend weighting and trimming to longitudinal data via stochastic ``flip'' interventions, which maintain the treatment status of subjects who would have received…

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