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Understanding the Risks and Rewards of Combining Unbiased and Possibly Biased Estimators, with Applications to Causal Inference

组合无偏与可能有偏估计量的风险和收益:因果推断应用

Several problems in statistics involve the combination of high-variance unbiased estimators with low-variance estimators that are only unbiased under strong assumptions. A notable example is the estimation of causal effects while combining small experimental datasets with larger observational datasets. There exist a series of recent proposals on how to perform such a combination, even when the bias of the low-variance estimator is unknown. To build intuition for the…

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Restricted Mean Survival Time Estimation Using Bayesian Nonparametric Dependent Mixture Models

利用贝叶斯非参数依赖混合模型估计限制平均生存时间

Restricted mean survival time (RMST) is an intuitive summary statistic for time-to-event random variables, and can be used for measuring treatment effects. Compared to hazard ratio, its estimation procedure is robust against the non-proportional hazards assumption. We propose nonparametric Bayeisan (BNP) estimators for RMST using a dependent stick-breaking process prior mixture model that adjusts for mixed-type covariates. The proposed Bayesian estimators can yield both…

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Statistical causal inference methods for observational research in PER: a primer

物理教育观察研究中的统计因果推断方法入门

Recent critiques of Physics Education Research (PER) studies have revoiced the critical issues when drawing causal inferences from observational data where no intervention is present. In response to a call for a "causal reasoning primer", this paper discusses some of the fundamental issues underlying statistical causal inference. In reviewing these issues, we discuss well-established causal inference methods commonly applied in other fields and discuss their application to…

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Change point detection in dynamic Gaussian graphical models: the impact of COVID-19 pandemic on the US stock market

动态高斯图模型的变点检测:新冠疫情期间美国股市的依赖变化

Reliable estimates of volatility and correlation are fundamental in economics and finance for understanding the impact of macroeconomics events on the market and guiding future investments and policies. Dependence across financial returns is likely to be subject to sudden structural changes, especially in correspondence with major global events, such as the COVID-19 pandemic. In this work, we are interested in capturing abrupt changes over time in the dependence across US…

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A nonparametric doubly robust test for a continuous treatment effect

连续处理效应的非参数双重稳健检验

The vast majority of literature on evaluating the significance of a treatment effect based on observational data has been confined to discrete treatments. These methods are not applicable to drawing inference for a continuous treatment, which arises in many important applications. To adjust for confounders when evaluating a continuous treatment, existing inference methods often rely on discretizing the treatment or using (possibly misspecified) parametric models for the…

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On the estimation of locally stationary functional time series

局部平稳函数型时间序列的估计

This study develops an asymptotic theory for estimating the time-varying characteristics of locally stationary functional time series (LSFTS). We investigate a kernel-based method to estimate the time-varying covariance operator and the time-varying mean function of an LSFTS. In particular, we derive the convergence rate of the kernel estimator of the covariance operator and associated eigenvalue and eigenfunctions and establish a central limit theorem for the kernel-based…

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Extreme Changes in Changes

极端分位数的变化中的变化估计

Policy analysts are often interested in treating the units with extreme outcomes, such as infants with extremely low birth weights. Existing changes-in-changes (CIC) estimators are tailored to middle quantiles and do not work well for such subpopulations. This paper proposes a new CIC estimator to accurately estimate treatment effects at extreme quantiles. With its asymptotic normality, we also propose a method of statistical inference, which is simple to implement. Based on…

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Stable Outcomes and Information in Games: An Empirical Framework

博弈中的稳定结果与信息:一个实证框架

Empirically, many strategic settings are characterized by stable outcomes in which players' decisions are publicly observed, yet no player takes the opportunity to deviate. To analyze such situations in the presence of incomplete information, we build an empirical framework by introducing a novel solution concept that we call Bayes stable equilibrium. Our framework allows the researcher to be agnostic about players' information and the equilibrium selection rule. The Bayes…

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On true versus estimated propensity scores for treatment effect estimation with discrete controls

离散控制变量下处理效应估计中的真实与估计倾向得分

The finite sample variance of an inverse propensity weighted estimator is derived in the case of discrete control variables with finite support. The obtained expressions generally corroborate widely-cited asymptotic theory showing that estimated propensity scores are superior to true propensity scores in the context of inverse propensity weighting. However, similar analysis of a modified estimator demonstrates that foreknowledge of the true propensity function can confer a…

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Double Robust Semi-Supervised Inference for the Mean: Selection Bias under MAR Labeling with Decaying Overlap

重叠衰减与随机缺失标注选择偏差下的双重稳健半监督均值推断

Semi-supervised (SS) inference has received much attention in recent years. Apart from a moderate-sized labeled data, L, the SS setting is characterized by an additional, much larger sized, unlabeled data, U. The setting of |U| >> |L|, makes SS inference unique and different from the standard missing data problems, owing to natural violation of the so-called "positivity" or "overlap" assumption. However, most of the SS literature implicitly assumes L and U to be equally…

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Functional Connectivity: Continuous-Time Latent Factor Models for Neural Spike Trains

神经脉冲序列功能连接的连续时间潜因子模型

Modelling the dynamics of interactions in a neuronal ensemble is an important problem in functional connectivity research. One popular framework is latent factor models (LFMs), which have achieved notable success in decoding neuronal population dynamics. However, most LFMs are specified in discrete time, where the choice of bin size significantly impacts inference results. In this work, we present what is, to the best of our knowledge, the first continuous-time multivariate…

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Evaluating Dynamic Conditional Quantile Treatment Effects with Applications in Ridesharing

动态条件分位数处理效应的评估及网约车应用

Many modern tech companies, such as Google, Uber, and Didi, utilize online experiments (also known as A/B testing) to evaluate new policies against existing ones. While most studies concentrate on average treatment effects, situations with skewed and heavy-tailed outcome distributions may benefit from alternative criteria, such as quantiles. However, assessing dynamic quantile treatment effects (QTE) remains a challenge, particularly when dealing with data from ride-sourcing…

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Long Memory of Max-Stable Time Series as Phase Transition: Asymptotic Behaviour of Tail Dependence Estimators

最大稳定时间序列长记忆的相变与尾部依赖估计量渐近行为

In this paper, we consider a simple estimator for tail dependence coefficients of a max-stable time series and show its asymptotic normality under a mild condition. The novelty of our result is that this condition does not involve mixing properties that are common in the literature. More importantly, our condition is linked to the transition between long and short range dependence (LRD/SRD) for max-stable time series. This is based on a recently proposed notion of LRD in the…

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Efficient Estimation for Staggered Rollout Designs

交错实施设计中的高效估计

We study estimation of causal effects in staggered rollout designs, i.e. settings where there is staggered treatment adoption and the timing of treatment is as-good-as randomly assigned. We derive the most efficient estimator in a class of estimators that nests several popular generalized difference-in-differences methods. A feasible plug-in version of the efficient estimator is asymptotically unbiased with efficiency (weakly) dominating that of existing approaches. We…

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Monitoring multicountry macroeconomic risk

多国宏观经济风险监测

We propose a multicountry quantile factor augmeneted vector autoregression (QFAVAR) to model heterogeneities both across countries and across characteristics of the distributions of macroeconomic time series. The presence of quantile factors allows for summarizing these two heterogeneities in a parsimonious way. We develop two algorithms for posterior inference that feature varying level of trade-off between estimation precision and computational speed. Using monthly data…

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A Guide to Regression Discontinuity Designs in Medical Applications

医学应用中的回归不连续设计指南

We present a practical guide for the analysis of regression discontinuity (RD) designs in biomedical contexts. We begin by introducing key concepts, assumptions, and estimands within both the continuity-based framework and the local randomization framework. We then discuss modern estimation and inference methods within both frameworks, including approaches for bandwidth or local neighborhood selection, optimal treatment effect point estimation, and robust bias-corrected…

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High-dimensional Inference for Dynamic Treatment Effects

高维动态处理效应的统计推断

Estimating dynamic treatment effects is a crucial endeavor in causal inference, particularly when confronted with high-dimensional confounders. Doubly robust (DR) approaches have emerged as promising tools for estimating treatment effects due to their flexibility. However, we showcase that the traditional DR approaches that only focus on the DR representation of the expected outcomes may fall short of delivering optimal results. In this paper, we propose a novel DR…

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A Causal Inference Framework for Leveraging External Controls in Hybrid Trials

混合试验中利用外部对照的因果推断框架

We consider the challenges associated with causal inference in settings where data from a randomized trial is augmented with control data from an external source to improve efficiency in estimating the average treatment effect (ATE). Through the development of a formal causal inference framework, we outline sufficient causal assumptions about the exchangeability between the internal and external controls to identify the ATE and establish the connection to a novel graphical…

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An Improved Doubly Robust Estimator Using Partially Recovered Unmeasured Spatial Confounder

利用部分恢复的未测空间混杂变量改进双重稳健估计

Studies in environmental and epidemiological sciences are often spatially varying and observational in nature with the aim of establishing cause and effect relationships. One of the major challenges with such studies is the presence of unmeasured spatial confounders. 'spatial confounding' is the phenomenon in which the spatial residuals are correlated to the spatial covariates in the model, when unaccounted for it can lead to biased causal effect estimates. This paper…

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Estimation and Inference in Threshold Predictive Regression Models with Locally Explosive Regressors

局部爆炸解释变量下门限预测回归模型的估计与推断

In this paper, we study the estimation of the threshold predictive regression model with hybrid stochastic local unit root predictors. We demonstrate the estimation procedure and derive the asymptotic distribution of the least square estimator and the IV based estimator proposed by Magdalinos and Phillips (2009), under the null hypothesis of a diminishing threshold effect. Simulation experiments focus on the finite sample performance of our proposed estimators and the…

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Semiparametrically Optimal Cointegration Test

半参数最优协整检验

This paper aims to address the issue of semiparametric efficiency for cointegration rank testing in finite-order vector autoregressive models, where the innovation distribution is considered an infinite-dimensional nuisance parameter. Our asymptotic analysis relies on Le Cam's theory of limit experiment, which in this context takes the form of Locally Asymptotically Brownian Functional (LABF). By leveraging the structural version of LABF, an Ornstein-Uhlenbeck experiment, we…

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An Application of the Causal Roadmap in Two Safety Monitoring Case Studies: Covariate-Adjustment and Outcome Prediction using Electronic Health Record Data

因果路线图在两项安全监测案例中的应用:电子病历协变量调整与结局预测

Real-world data, such as administrative claims and electronic health records, are increasingly used for safety monitoring and to help guide regulatory decision-making. In these settings, it is important to document analytic decisions transparently and objectively to ensure that analyses meet their intended goals. The Causal Roadmap is an established framework that can guide and document analytic decisions through each step of the analytic pipeline, which will help…

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Causal Inference with Unmeasured Confounding from Nonignorable Missing Outcomes

不可忽略结局缺失与未测混杂下的因果推断

Observational studies are the primary source of data for causal inference, but it is challenging when existing unmeasured confounding. Missing data problems are also common in observational studies. How to obtain the causal effects from the nonignorable missing data with unmeasured confounding is a challenge. In this paper, we consider that how to obtain complier average causal effect with unmeasured confounding from the nonignorable missing outcomes. We propose an auxiliary…

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Decomposition of Differences in Distribution under Sample Selection and the Gender Wage Gap

样本选择下的分布差异分解与性别工资差距

I address the decomposition of the differences between the distribution of outcomes of two groups when individuals self-select themselves into participation. I differentiate between the decomposition for participants and the entire population, highlighting how the primitive components of the model affect each of the distributions of outcomes. Additionally, I introduce two ancillary decompositions that help uncover the sources of differences in the distribution of…

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