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Group Sequential Testing of a Treatment Effect Using a Surrogate Marker

利用替代指标对处理效应进行群序贯检验

The identification of surrogate markers is motivated by their potential to make decisions sooner about a treatment effect. However, few methods have been developed to actually use a surrogate marker to test for a treatment effect in a future study. Most existing methods consider combining surrogate marker and primary outcome information to test for a treatment effect, rely on fully parametric methods where strict parametric assumptions are made about the relationship between…

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Tensor Time Series Imputation through Tensor Factor Modelling

基于张量因子模型的张量时间序列缺失值插补

We propose tensor time series imputation when the missing pattern in the tensor data can be general, as long as any two data positions along a tensor fibre are both observed for enough time points. The method is based on a tensor time series factor model with Tucker decomposition of the common component. One distinguished feature of the tensor time series factor model used is that there can be weak factors in the factor loadings matrix for each mode. This reflects reality…

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Bridging multiple worlds: multi-marginal optimal transport for causal partial-identification problem

连接多个潜在世界:因果部分识别的多边际最优传输方法

Under the prevalent potential outcome model in causal inference, each unit is associated with multiple potential outcomes but at most one of which is observed, leading to many causal quantities being only partially identified. The inherent missing data issue echoes the multi-marginal optimal transport (MOT) problem, where marginal distributions are known, but how the marginals couple to form the joint distribution is unavailable. In this paper, we cast the causal partial…

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Joint spatial modeling of mean and non-homogeneous variance combining semiparametric SAR and GAMLSS models for hedonic prices

结合半参数 SAR 与 GAMLSS 的特征价格均值和异质方差空间建模

In the context of spatial econometrics, it is very useful to have methodologies that allow modeling the spatial dependence of the observed variables and obtaining more precise predictions of both the mean and the variability of the response variable, something very useful in territorial planning and public policies. This paper proposes a new methodology that jointly models the mean and the variance. Also, it allows to model the spatial dependence of the dependent variable as…

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High-dimensional regression with a count response

计数响应的高维回归

We consider high-dimensional regression with a count response modeled by Poisson or negative binomial generalized linear model (GLM). We propose a penalized maximum likelihood estimator with a properly chosen complexity penalty and establish its adaptive minimaxity across models of various sparsity. To make the procedure computationally feasible for high-dimensional data we consider its LASSO and SLOPE convex surrogates. Their performance is illustrated through simulated and…

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Cubature-based uncertainty estimation for nonlinear regression models

基于稀疏网格求积的非线性回归不确定性估计

Calibrating model parameters to measured data by minimizing loss functions is an important step in obtaining realistic predictions from model-based approaches, e.g., for process optimization. This is applicable to both knowledge-driven and data-driven model setups. Due to measurement errors, the calibrated model parameters also carry uncertainty. In this contribution, we use cubature formulas based on sparse grids to calculate the variance of the regression results. The…

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Concentration of a sparse Bayesian model with Horseshoe prior in estimating high-dimensional precision matrix

稀疏贝叶斯 Horseshoe 先验在高维精度矩阵估计中的集中性

Precision matrices are crucial in many fields such as social networks, neuroscience, and economics, representing the edge structure of Gaussian graphical models (GGMs), where a zero in an off-diagonal position of the precision matrix indicates conditional independence between nodes. In high-dimensional settings where the dimension of the precision matrix \( p \) exceeds the sample size \( n \) and the matrix is sparse, methods like graphical Lasso, graphical SCAD, and CLIME…

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Machine Learning and Econometric Approaches to Fiscal Policies: Understanding Industrial Investment Dynamics in Uruguay (1974-2010)

财政政策的机器学习与计量分析:乌拉圭工业投资动态

This paper examines the impact of fiscal incentives on industrial investment in Uruguay from 1974 to 2010. Using a mixed-method approach that combines econometric models with machine learning techniques, the study investigates both the short-term and long-term effects of fiscal benefits on industrial investment. The results confirm the significant role of fiscal incentives in driving long-term industrial growth, while also highlighting the importance of a stable…

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Using LASSO for Variable Selection in Exponential Random Graph models

使用LASSO进行指数随机图模型的变量选择

The paper demonstrates the use of LASSO-based estimation in network models. Taking the Exponential Random Graph Model (ERGM) as a flexible and widely used model for network data analysis, the paper focuses on the question of how to specify the (sufficient) statistics, that define the model structure. This includes both, endogenous network statistics (e.g. twostars, triangles, etc.) as well as statistics involving exogenous covariates; on the node as well as on the edge…

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Identifiable causal inference with noisy treatment and no side information

处理变量含噪且无辅助信息时的可识别因果推断

In some causal inference scenarios, the treatment variable is measured inaccurately, for instance in epidemiology or econometrics. Failure to correct for the effect of this measurement error can lead to biased causal effect estimates. Previous research has not studied methods that address this issue from a causal viewpoint while allowing for complex nonlinear dependencies and without assuming access to side information. For such a scenario, this study proposes a model that…

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Randomized Spline Trees for Functional Data Classification: Theory and Application to Environmental Time Series

函数型数据分类的随机样条树:理论与环境时间序列应用

Functional data analysis (FDA) and ensemble learning can be powerful tools for analyzing complex environmental time series. Recent literature has highlighted the key role of diversity in enhancing accuracy and reducing variance in ensemble methods.This paper introduces Randomized Spline Trees (RST), a novel algorithm that bridges these two approaches by incorporating randomized functional representations into the Random Forest framework. RST generates diverse functional…

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Identification and multiply robust estimation in causal mediation analysis across principal strata

主分层间因果中介分析的识别与多重稳健估计

We consider assessing causal mediation in the presence of a post-treatment event (examples include noncompliance, a clinical event, or death). We identify natural mediation effects for the entire study population and for each principal stratum characterized by the joint potential values of the post-treatment event. We derive the efficient influence function for each mediation estimand, which motivates a set of multiply robust estimators for inference. The multiply robust…

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How to achieve model-robust inference in stepped wedge trials with model-based methods?

如何用模型方法实现阶梯楔形试验的模型稳健推断?

A stepped wedge design is a unidirectional crossover design where clusters are randomized to distinct treatment sequences. While model-based analysis of stepped wedge designs is standard practice to evaluate treatment effects accounting for clustering and adjusting for covariates, their properties under misspecification have not been systematically explored. In this article, we focus on model-based methods, including linear mixed models and generalized estimating equations…

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Estimation and Inference for Three-Dimensional Panel Data Models

三维面板数据模型的估计与推断

Hierarchical panel data models have recently garnered significant attention. This study contributes to the relevant literature by introducing a novel three-dimensional (3D) hierarchical panel data model, which integrates panel regression with three sets of latent factor structures: one set of global factors and two sets of local factors. Instead of aggregating latent factors from various nodes, as seen in the literature of distributed principal component analysis (PCA), we…

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Determining number of factors under stability considerations

基于稳定性考量确定因子数量

This paper proposes a novel method for determining the number of factors in linear factor models under stability considerations. An instability measure is proposed based on the principal angle between the estimated loading spaces obtained by data splitting. Based on this measure, criteria for determining the number of factors are proposed and shown to be consistent. This consistency is obtained using results from random matrix theory, especially the complete delocalization…

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Bayesian inference of vector autoregressions with tensor decompositions

利用张量分解的向量自回归贝叶斯推断

Vector autoregressions (VARs) are popular model for analyzing multivariate economic time series. However, VARs can be over-parameterized if the numbers of variables and lags are moderately large. Tensor VAR, a recent solution to over-parameterization, treats the coefficient matrix as a third-order tensor and estimates the corresponding tensor decomposition to achieve parsimony. In this paper, we employ the Tensor VAR structure with a CANDECOMP/PARAFAC (CP) decomposition and…

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Debiased high-dimensional regression calibration for errors-in-variables log-contrast models

高维成分数据变量误差对数对比模型的去偏回归校准

Motivated by the challenges in analyzing gut microbiome and metagenomic data, this work aims to tackle the issue of measurement errors in high-dimensional regression models that involve compositional covariates. This paper marks a pioneering effort in conducting statistical inference on high-dimensional compositional data affected by mismeasured or contaminated data. We introduce a calibration approach tailored for the linear log-contrast model. Under relatively lenient…

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Asymptotics of Stochastic Gradient Descent with Dropout Regularization in Linear Models

线性模型中带 Dropout 正则化的随机梯度下降渐近理论

This paper proposes an asymptotic theory for online inference of the stochastic gradient descent (SGD) iterates with dropout regularization in linear regression. Specifically, we establish the geometric-moment contraction (GMC) for constant step-size SGD dropout iterates to show the existence of a unique stationary distribution of the dropout recursive function. By the GMC property, we provide quenched central limit theorems (CLT) for the difference between dropout and $\ell^2$…

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The First-stage F Test with Many Weak Instruments

大量弱工具变量下的第一阶段 F 检验

A widely adopted approach for detecting weak instruments is to use the first-stage $F$ statistic. While this method was developed with a fixed number of instruments, its performance with many instruments remains insufficiently explored. We show that the first-stage $F$ test exhibits distorted sizes for detecting many weak instruments, regardless of the choice of pretested estimators or Wald tests. These distortions occur due to the inadequate approximation using classical…

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Testing for a Forecast Accuracy Breakdown under Long Memory

长记忆条件下预测准确性失稳的检验

We propose a test to detect a forecast accuracy breakdown in a long memory time series and provide theoretical and simulation evidence on the memory transfer from the time series to the forecast residuals. The proposed method uses a double sup-Wald test against the alternative of a structural break in the mean of an out-of-sample loss series. To address the problem of estimating the long-run variance under long memory, a robust estimator is applied. The corresponding…

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Anytime-Valid Inference for Double/Debiased Machine Learning of Causal Parameters

因果参数双重去偏机器学习的任意时点有效推断

Double (debiased) machine learning (DML) has seen widespread use in recent years for learning causal/structural parameters, in part due to its flexibility and adaptability to high-dimensional nuisance functions as well as its ability to avoid bias from regularization or overfitting. However, the classic double-debiased framework is only valid asymptotically for a predetermined sample size, thus lacking the flexibility of collecting more data if sharper inference is needed,…

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Cross-validation on Extreme Regions

极端区域上的交叉验证

We conduct a non asymptotic study of the Cross Validation (CV) estimate of the generalization risk for learning algorithms dedicated to extreme regions of the covariates space. In this Extreme Value Analysis context, the risk function measures the algorithm's error given that the norm of the input exceeds a high quantile. The main challenge within this framework is the negligible size of the extreme training sample with respect to the full sample size and the necessity to…

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Estimation and Inference for Causal Functions with Multiway Clustered Data

多维聚类数据下因果函数的估计与推断

This paper proposes methods of estimation and uniform inference for a general class of causal functions, such as the conditional average treatment effects and the continuous treatment effects, under multiway clustering. The causal function is identified as a conditional expectation of an adjusted (Neyman-orthogonal) signal that depends on high-dimensional nuisance parameters. We propose a two-step procedure where the first step uses machine learning to estimate the…

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Optimal Regularization for a Data Source

数据源的最优正则化

In optimization-based approaches to inverse problems and to statistical estimation, it is common to augment criteria that enforce data fidelity with a regularizer that promotes desired structural properties in the solution. The choice of a suitable regularizer is typically driven by a combination of prior domain information and computational considerations. Convex regularizers are attractive computationally but they are limited in the types of structure they can promote. On…

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