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Counterfactual Copula and Its Application to the Effects of College Education on Intergenerational Mobility

反事实 Copula 及其在大学教育与代际流动研究中的应用

This paper proposes a nonparametric estimator of the counterfactual copula of two outcome variables that would be affected by a policy intervention. The proposed estimator allows policymakers to conduct ex-ante evaluations by comparing the estimated counterfactual and actual copulas as well as their corresponding measures of association. Asymptotic properties of the counterfactual copula estimator are established under regularity conditions. These conditions are also used to…

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Distributional Vector Autoregression: Eliciting Macro and Financial Dependence

分布向量自回归:刻画宏观与金融依赖关系

Vector autoregression is an essential tool in empirical macroeconomics and finance for understanding the dynamic interdependencies among multivariate time series. In this study, we expand the scope of vector autoregression by incorporating a multivariate distributional regression framework and introducing a distributional impulse response function, providing a comprehensive view of dynamic heterogeneity. We propose a straightforward yet flexible estimation method and…

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Educational Inequality of Opportunity and Mobility in Europe

欧洲教育机会不平等与代际流动

Educational attainment generates labor market returns, societal gains and has intrinsic value for individuals. We study Inequality of Opportunity (IOp) and intergenerational mobility in the distribution of educational attainment. We propose to use debiased IOp estimators based on the Gini coefficient and the Mean Logarithmic Deviation (MLD) which are robust to machine learning biases. We also measure the effect of each circumstance on IOp, we provide tests to compare IOp in…

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Censored Quantile Regression with Many Controls

含大量控制变量的删失分位数回归

This paper develops estimation and inference methods for censored quantile regression models with high-dimensional controls. The methods are based on the application of double/debiased machine learning (DML) framework to the censored quantile regression estimator of Buchinsky and Hahn (1998). I provide valid inference for low-dimensional parameters of interest in the presence of high-dimensional nuisance parameters when implementing machine learning estimators. The proposed…

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ARMA Model Development and Analysis for Global Temperature Uncertainty

全球温度不确定性的 ARMA 模型构建与分析

Temperature uncertainty models for land and sea surfaces can be developed based on statistical methods. In this paper, we developed a novel time series temperature uncertainty model which is the Auto-regressive Moving Average (ARMA)(1, 1) model. The model was developed for observed annual mean temperature anomaly X(t) which is a combination of true (latent) global anomaly Y (t) for a year (t) and normal variable w(t). The uncertainty is taken as the variance of w(t) which…

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Identification and Estimation of Categorical Random Coefficient Models

类别型随机系数模型的识别与估计

This paper proposes a linear categorical random coefficient model, in which the random coefficients follow parametric categorical distributions. The distributional parameters are identified based on a linear recurrence structure of moments of the random coefficients. A Generalized Method of Moments estimation procedure is proposed also employed by Peter Schmidt and his coauthors to address heterogeneity in time effects in panel data models. Using Monte Carlo simulations, we…

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Estimating heterogeneous treatment effects with right-censored data via causal survival forests

利用因果生存森林估计右删失数据中的异质性处理效应

Forest-based methods have recently gained in popularity for non-parametric treatment effect estimation. Building on this line of work, we introduce causal survival forests, which can be used to estimate heterogeneous treatment effects in a survival and observational setting where outcomes may be right-censored. Our approach relies on orthogonal estimating equations to robustly adjust for both censoring and selection effects under unconfoundedness. In our experiments, we find…

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Recovering Sparse and Interpretable Subgroups with Heterogeneous Treatment Effects with Censored Time-to-Event Outcomes

删失事件时间结局下具有异质处理效应的稀疏可解释亚群识别

Studies involving both randomized experiments as well as observational data typically involve time-to-event outcomes such as time-to-failure, death or onset of an adverse condition. Such outcomes are typically subject to censoring due to loss of follow-up and established statistical practice involves comparing treatment efficacy in terms of hazard ratios between the treated and control groups. In this paper we propose a statistical approach to recovering sparse phenogroups…

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Flexible and Efficient Contextual Bandits with Heterogeneous Treatment Effect Oracles

借助异质性处理效应估计器构建灵活高效的情境老虎机算法

Contextual bandit algorithms often estimate reward models to inform decision-making. However, true rewards can contain action-independent redundancies that are not relevant for decision-making. We show it is more data-efficient to estimate any function that explains the reward differences between actions, that is, the treatment effects. Motivated by this observation, building on recent work on oracle-based bandit algorithms, we provide the first reduction of contextual…

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Inference on Individual Treatment Effects in Nonseparable Triangular Models

非可分三角模型中个体处理效应的统计推断

In nonseparable triangular models with a binary endogenous treatment and a binary instrumental variable, Vuong and Xu (2017) established identification results for individual treatment effects (ITEs) under the rank invariance assumption. Using their approach, Feng, Vuong, and Xu (2019) proposed a uniformly consistent kernel estimator for the density of the ITE that utilizes estimated ITEs. In this paper, we establish the asymptotic normality of the density estimator of Feng,…

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Structural Break Detection in Quantile Predictive Regression Models with Persistent Covariates

持久协变量下分位数预测回归模型的结构突变检测

We propose an econometric environment for structural break detection in nonstationary quantile predictive regressions. We establish the limit distributions for a class of Wald and fluctuation type statistics based on both the ordinary least squares estimator and the endogenous instrumental regression estimator proposed by Phillips and Magdalinos (2009a, Econometric Inference in the Vicinity of Unity. Working paper, Singapore Management University). Although the asymptotic…

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Extensions for Inference in Difference-in-Differences with Few Treated Clusters

少量处理簇下双重差分推断的扩展

In settings with few treated units, Difference-in-Differences (DID) estimators are not consistent, and are not generally asymptotically normal. This poses relevant challenges for inference. While there are inference methods that are valid in these settings, some of these alternatives are not readily available when there is variation in treatment timing and heterogeneous treatment effects; or for deriving uniform confidence bands for event-study plots. We present alternatives…

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Confounding-adjustment methods for the causal difference in medians

因果中位数差的混杂调整方法

With continuous outcomes, the average causal effect is typically defined using a contrast of expected potential outcomes. However, in the presence of skewed outcome data, the expectation may no longer be meaningful. In practice the typical approach is to either "ignore or transform" - ignore the skewness altogether or transform the outcome to obtain a more symmetric distribution, although neither approach is entirely satisfactory. Alternatively the causal effect can be…

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Augmented Learning of Heterogeneous Treatment Effects via Gradient Boosting Trees

基于梯度提升树的异质性处理效应增广学习

Heterogeneous treatment effects (HTE) based on patients' genetic or clinical factors are of significant interest to precision medicine. Simultaneously modeling HTE and corresponding main effects for randomized clinical trials with high-dimensional predictive markers is challenging. Motivated by the modified covariates approach, we propose a two-stage statistical learning procedure for estimating HTE with optimal efficiency augmentation, generalizing to arbitrary interaction…

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Instrumental variable quantile regression under random right censoring

随机右删失下的工具变量分位数回归

This paper studies a semiparametric quantile regression model with endogenous variables and random right censoring. The endogeneity issue is solved using instrumental variables. It is assumed that the structural quantile of the logarithm of the outcome variable is linear in the covariates and censoring is independent. The regressors and instruments can be either continuous or discrete. The specification generates a continuum of equations of which the quantile regression…

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Heterogeneous Synthetic Learner for Panel Data

面板数据的异质性合成学习器

In the new era of personalization, learning the heterogeneous treatment effect (HTE) becomes an inevitable trend with numerous applications. Yet, most existing HTE estimation methods focus on independently and identically distributed observations and cannot handle the non-stationarity and temporal dependency in the common panel data setting. The treatment evaluators developed for panel data, on the other hand, typically ignore the individualized information. To fill the gap,…

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Causal Inference under Data Restrictions

数据受限条件下的因果推断

This dissertation focuses on modern causal inference under uncertainty and data restrictions, with applications to neoadjuvant clinical trials, distributed data networks, and robust individualized decision making. In the first project, we propose a method under the principal stratification framework to identify and estimate the average treatment effects on a binary outcome, conditional on the counterfactual status of a post-treatment intermediate response. Under mild…

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An MCMC Approach to Classical Estimation

通过 MCMC 实现经典估计的方法

This paper studies computationally and theoretically attractive estimators called the Laplace type estimators (LTE), which include means and quantiles of Quasi-posterior distributions defined as transformations of general (non-likelihood-based) statistical criterion functions, such as those in GMM, nonlinear IV, empirical likelihood, and minimum distance methods. The approach generates an alternative to classical extremum estimation and also falls outside the parametric…

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Optimal Transport for Counterfactual Estimation: A Method for Causal Inference

用于反事实估计的最优传输方法

Many problems ask a question that can be formulated as a causal question: "what would have happened if...?" For example, "would the person have had surgery if he or she had been Black?" To address this kind of questions, calculating an average treatment effect (ATE) is often uninformative, because one would like to know how much impact a variable (such as skin color) has on a specific individual, characterized by certain covariates. Trying to calculate a conditional ATE…

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Robust M-Estimation for Additive Single-Index Cointegrating Time Series Models

加性单指标协整时间序列模型的稳健 M 估计

Robust M-estimation uses loss functions, such as least absolute deviation (LAD), quantile loss and Huber's loss, to construct its objective function, in order to for example eschew the impact of outliers, whereas the difficulty in analysing the resultant estimators rests on the nonsmoothness of these losses. Generalized functions have advantages over ordinary functions in several aspects, especially generalized functions possess derivatives of any order. Generalized…

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Resampling techniques for a class of smooth, possibly data-adaptive empirical copulas

平滑且可数据自适应的经验 Copula 重抽样方法

We investigate the validity of two resampling techniques when carrying out inference on the underlying unknown copula using a recently proposed class of smooth, possibly data-adaptive nonparametric estimators that contains empirical Bernstein copulas (and thus the empirical beta copula). Following \cite{KirSegTsu21}, the first resampling technique is based on drawing samples from the smooth estimator and can only can be used in the case of independent observations. The…

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Neural Spline Search for Quantile Probabilistic Modeling

用于分位数概率建模的神经样条搜索

Accurate estimation of output quantiles is crucial in many use cases, where it is desired to model the range of possibility. Modeling target distribution at arbitrary quantile levels and at arbitrary input attribute levels are important to offer a comprehensive picture of the data, and requires the quantile function to be expressive enough. The quantile function describing the target distribution using quantile levels is critical for quantile regression. Although various…

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Quantile Autoregression-based Non-causality Testing

基于分位数自回归的非因果性检验

Non-causal processes have been drawing attention recently in Macroeconomics and Finance for their ability to display nonlinear behaviors such as asymmetric dynamics, clustering volatility, and local explosiveness. In this paper, we investigate the statistical properties of empirical conditional quantiles of non-causal processes. Specifically, we show that the quantile autoregression (QAR) estimates for non-causal processes do not remain constant across different quantiles in…

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Inference for Low-Rank Models

低秩模型的统计推断

This paper studies inference in linear models with a high-dimensional parameter matrix that can be well-approximated by a ``spiked low-rank matrix.'' A spiked low-rank matrix has rank that grows slowly compared to its dimensions and nonzero singular values that diverge to infinity. We show that this framework covers a broad class of models of latent-variables which can accommodate matrix completion problems, factor models, varying coefficient models, and heterogeneous…

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