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Estimating Time-Varying Direct and Indirect Causal Excursion Effects with Longitudinal Binary Outcomes

纵向二元结局的时变直接与间接因果偏离效应估计

Construction of just-in-time adaptive interventions, such as prompts delivered by mobile apps to promote and maintain behavioral change, requires knowledge about time-varying moderated effects to inform when and how we deliver intervention options. Micro-randomized trials (MRT) have emerged as a sequentially randomized design to gather requisite data for effect estimation. The existing literature (Qian et al., 2020; Boruvka et al., 2018; Dempsey et al., 2020) has defined a…

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Power analyses for stepped wedge designs with multivariate continuous outcomes

多元连续结局阶梯楔形设计的功效分析

Multivariate outcomes are common in pragmatic cluster randomized trials. While sample size calculation procedures for multivariate outcomes exist under parallel assignment, none have been developed for a stepped wedge design. In this article, we present computationally efficient power and sample size procedures for stepped wedge cluster randomized trials (SW-CRTs) with multivariate outcomes that differentiate the within-period and between-period intracluster correlation…

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Estimation and Inference in Factor Copula Models with Exogenous Covariates

含外生协变量的因子 Copula 模型:估计与推断

A factor copula model is proposed in which factors are either simulable or estimable from exogenous information. Point estimation and inference are based on a simulated methods of moments (SMM) approach with non-overlapping simulation draws. Consistency and limiting normality of the estimator is established and the validity of bootstrap standard errors is shown. Doing so, previous results from the literature are verified under low-level conditions imposed on the individual…

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Bounds for Treatment Effects in the Presence of Anticipatory Behavior

存在预期行为时处理效应的界限

In program evaluations, units can often anticipate the implementation of a new policy before it occurs. Such anticipatory behavior can lead to units' outcomes becoming dependent on their future treatment assignments. In this paper, I employ a potential-outcomes framework to analyze the treatment effect with anticipation. I start with a classical difference-in-differences model with two time periods and provide identified sets with easy-to-implement estimation and inference…

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Vector causal inference between two groups of variables

两组变量之间的向量因果推断

Methods to identify cause-effect relationships currently mostly assume the variables to be scalar random variables. However, in many fields the objects of interest are vectors or groups of scalar variables. We present a new constraint-based non-parametric approach for inferring the causal relationship between two vector-valued random variables from observational data. Our method employs sparsity estimates of directed and undirected graphs and is based on two new principles…

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Functional estimation and change detection for nonstationary time series

非平稳时间序列的泛函估计与变化检测

Tests for structural breaks in time series should ideally be sensitive to breaks in the parameter of interest, while being robust to nuisance changes. Statistical analysis thus needs to allow for some form of nonstationarity under the null hypothesis of no change. In this paper, estimators for integrated parameters of locally stationary time series are constructed and a corresponding functional central limit theorem is established, enabling change-point inference for a broad…

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The Econometrics of Financial Duration Modeling

金融持续时间建模的计量经济学

We establish new results for estimation and inference in financial durations models, where events are observed over a given time span, such as a trading day, or a week. For the classical autoregressive conditional duration (ACD) models by Engle and Russell (1998, Econometrica 66, 1127-1162), we show that the large sample behavior of likelihood estimators is highly sensitive to the tail behavior of the financial durations. In particular, even under stationarity, asymptotic…

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Inference in a class of optimization problems: Confidence regions and finite sample bounds on errors in coverage probabilities

一类优化问题的推断:置信区域与覆盖概率误差的有限样本界

This paper describes three methods for carrying out non-asymptotic inference on partially identified parameters that are solutions to a class of optimization problems. Applications in which the optimization problems arise include estimation under shape restrictions, estimation of models of discrete games, and estimation based on grouped data. The partially identified parameters are characterized by restrictions that involve the unknown population means of observed random…

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Identifying the Effect of Persuasion

说服效应的识别

This paper examines a commonly used measure of persuasion whose precise interpretation has been obscure in the literature. By using the potential outcome framework, we define the causal persuasion rate by a proper conditional probability of taking the action of interest with a persuasive message conditional on not taking the action without the message. We then formally study identification under empirically relevant data scenarios and show that the commonly adopted measure…

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On the statistical role of inexact matching in observational studies

观察性研究中非精确匹配的统计作用

In observational causal inference, exact covariate matching plays two statistical roles: (i) it effectively controls for bias due to measured confounding; (ii) it justifies assumption-free inference based on randomization tests. This paper shows that inexact covariate matching does not always play these same roles. We find that inexact matching often leaves behind statistically meaningful bias and that this bias renders standard randomization tests asymptotically invalid. We…

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Approximate Bayesian Computation via Classification

通过分类实现近似贝叶斯计算

Approximate Bayesian Computation (ABC) enables statistical inference in simulator-based models whose likelihoods are difficult to calculate but easy to simulate from. ABC constructs a kernel-type approximation to the posterior distribution through an accept/reject mechanism which compares summary statistics of real and simulated data. To obviate the need for summary statistics, we directly compare empirical distributions with a Kullback-Leibler (KL) divergence estimator…

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Asymmetric Dependence Measurement and Testing

非对称依赖关系的度量与检验

Measuring the (causal) direction and strength of dependence between two variables (events), Xi and Xj , is fundamental for all science. Our survey of decades-long literature on statistical dependence reveals that most assume symmetry in the sense that the strength of dependence of Xi on Xj exactly equals the strength of dependence of Xj on Xi. However, we show that such symmetry is often untrue in many real-world examples, being neither necessary nor sufficient. Vinod's…

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Causal Inference with Conditional Instruments using Deep Generative Models

利用深度生成模型与条件工具变量进行因果推断

The instrumental variable (IV) approach is a widely used way to estimate the causal effects of a treatment on an outcome of interest from observational data with latent confounders. A standard IV is expected to be related to the treatment variable and independent of all other variables in the system. However, it is challenging to search for a standard IV from data directly due to the strict conditions. The conditional IV (CIV) method has been proposed to allow a variable to…

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Nonparametric Estimation of the Continuous Treatment Effect with Measurement Error

存在测量误差的连续处理效应的非参数估计

We identify the average dose-response function (ADRF) for a continuously valued error-contaminated treatment by a weighted conditional expectation. We then estimate the weights nonparametrically by maximising a local generalised empirical likelihood subject to an expanding set of conditional moment equations incorporated into the deconvolution kernels. Thereafter, we construct a deconvolution kernel estimator of ADRF. We derive the asymptotic bias and variance of our ADRF…

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Causal identification for continuous-time stochastic processes

连续时间随机过程的因果识别

Many real-world processes are trajectories that may be regarded as continuous-time "functional data". Examples include patients' biomarker concentrations, environmental pollutant levels, and prices of stocks. Corresponding advances in data collection have yielded near continuous-time measurements, from e.g. physiological monitors, wearable digital devices, and environmental sensors. Statistical methodology for estimating the causal effect of a time-varying treatment,…

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Estimating a Causal Exposure Response Function with a Continuous Error-Prone Exposure: A Study of Fine Particulate Matter and All-Cause Mortality

连续暴露测量有误时的因果暴露—反应函数估计:细颗粒物与全因死亡

Numerous studies have examined the associations between long-term exposure to fine particulate matter (PM2.5) and adverse health outcomes. Recently, many of these studies have begun to employ high-resolution predicted PM2.5 concentrations, which are subject to measurement error. Previous approaches for exposure measurement error correction have either been applied in non-causal settings or have only considered a categorical exposure. Moreover, most procedures have failed to…

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Leveraging baseline covariates to analyze small cluster-randomized trials with a rare binary outcome

利用基线协变量分析罕见二元结局的小型整群随机试验

Cluster-randomized trials (CRTs) involve randomizing entire groups of participants -- called clusters -- to treatment arms but are often comprised of a limited or fixed number of available clusters. While covariate adjustment can account for chance imbalances between treatment arms and increase statistical efficiency in individually-randomized trials, analytical methods for individual-level covariate adjustment in small CRTs have received little attention to date. In this…

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Fast, Robust Inference for Linear Instrumental Variables Models using Self-Normalized Moments

利用自标准化矩的线性工具变量模型快速稳健推断

We propose and implement an approach to inference in linear instrumental variables models which is simultaneously robust and computationally tractable. Inference is based on self-normalization of sample moment conditions, and allows for (but does not require) many (relative to the sample size), weak, potentially invalid or potentially endogenous instruments, as well as for many regressors and conditional heteroskedasticity. Our coverage results are uniform and can deliver a…

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Targeting functional parameters with semiparametric Bayesian inference

以半参数贝叶斯推断直接针对泛函参数

Typical Bayesian inference requires parameter identification via likelihood parameterization, which has invited criticism for being less flexible than the Frequentist framework and subject to misspecification. Though misspecification may be avoided by functional parameter inference under a nonparametric model space, there does not exist a flexible Bayesian semiparametric model that would allow full control over the marginal prior over any general functional parameter. We…

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A Design-Based Approach to Spatial Correlation

空间相关的设计型分析方法

When observing spatial data, what standard errors should we report? With the finite population framework, we identify three channels of spatial correlation: sampling scheme, assignment design, and model specification. The Eicker-Huber-White standard error, the cluster-robust standard error, and the spatial heteroskedasticity and autocorrelation consistent standard error are compared under different combinations of the three channels. Then, we provide guidelines for whether…

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Using Proxies to Improve Forecast Evaluation

利用代理变量改进预测评价

Comparative evaluation of forecasts of statistical functionals relies on comparing averaged losses of competing forecasts after the realization of the quantity $Y$, on which the functional is based, has been observed. Motivated by high-frequency finance, in this paper we investigate how proxies $\tilde Y$ for $Y$ - say volatility proxies - which are observed together with $Y$ can be utilized to improve forecast comparisons. We extend previous results on robustness of loss…

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Confidence Interval Construction for Multivariate time series using Long Short Term Memory Network

利用长短期记忆网络构造多元时间序列预测区间

In this paper we propose a novel procedure to construct a confidence interval for multivariate time series predictions using long short term memory network. The construction uses a few novel block bootstrap techniques. We also propose an innovative block length selection procedure for each of these schemes. Two novel benchmarks help us to compare the construction of this confidence intervals by different bootstrap techniques. We illustrate the whole construction through S\&P…

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Kernel PCA for multivariate extremes

用于多元极值分析的核主成分分析

We propose kernel PCA as a method for analyzing the dependence structure of multivariate extremes and demonstrate that it can be a powerful tool for clustering and dimension reduction. Our work provides some theoretical insight into the preimages obtained by kernel PCA, demonstrating that under certain conditions they can effectively identify clusters in the data. We build on these new insights to characterize rigorously the performance of kernel PCA based on an extremal…

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Robust High-dimensional Tuning Free Multiple Testing

稳健的高维免调参多重检验

A stylized feature of high-dimensional data is that many variables have heavy tails, and robust statistical inference is critical for valid large-scale statistical inference. Yet, the existing developments such as Winsorization, Huberization and median of means require the bounded second moments and involve variable-dependent tuning parameters, which hamper their fidelity in applications to large-scale problems. To liberate these constraints, this paper revisits the…

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