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Inference on common trends in functional time series

函数型时间序列共同趋势的统计推断

We study statistical inference on unit roots and cointegration for time series in a Hilbert space. We develop statistical inference on the number of common stochastic trends embedded in the time series, i.e., the dimension of the nonstationary subspace. We also consider tests of hypotheses on the nonstationary and stationary subspaces themselves. The Hilbert space can be of an arbitrarily large dimension, and our methods remain asymptotically valid even when the time series…

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Uniform Confidence Bands for Infinite-Dimensional Partially Identified Parameters

无限维部分识别参数的一致置信带

Infinite-dimensional parameters are ubiquitous in empirical economics. This paper develops an Imbens--Manski--Stoye type confidence band for infinite-dimensional partially identified parameters. In particular, we propose multiplier bootstrap-based construction of a uniform confidence band. By employing approximation theorems for suprema of non-centered empirical processes indexed by possibly non-Donsker classes \citep{chernozhukov2016empirical}, we confirm the uniform…

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Placebo Discontinuity Design

安慰剂断点设计

Standard regression discontinuity design (RDD) models rely on the continuity of expected potential outcomes at the cutoff. The standard continuity assumption can be violated by strategic manipulation of the running variable, which is realistic when the cutoff is widely known and when the treatment of interest is a social program or government benefit. In this work, we identify the treatment effect despite such a violation, by leveraging a placebo treatment and a placebo…

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Two Layers of Instability in Causal Estimation

因果估计中的两层不稳定性

There is a precise sense in which drawing causal inferences from observational data is hard, even when identifiability is assumed. In particular, Robins and Ritov (1997) and Robins et al. (2003) showed that causal effects can be discontinuous as a function of the data distribution: two arbitrarily close data distributions might correspond to different causal effects. This is a fact independent of the choice of estimator; however, not all estimators are equally unstable. Our…

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Properties of the Conditional Likelihood Ratio Test under Discrete Approximation

离散近似下条件似然比检验的性质

The conditional likelihood ratio (CLR) test is a valuable tool for inference under weak identification, with appealing theoretical properties in both linear and non-linear settings. Its implementation nevertheless requires minimizing a non-convex objective function, a difficulty long recognized even in the linear IV setting. While grid-based methods that provide a practical approximation may perform well in particular designs, such procedures do not guarantee that the…

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Repeated sampling of different individuals within the same clusters to improve precision of longitudinal estimators: the DISC design

固定簇内重复抽取不同个体以提高纵向估计精度:DISC 设计

Background: Longitudinal studies often involve repeated cluster sampling of a population at multiple time points, such as in difference-in-differences (DID) studies. Although cohort designs typically lead to more efficient estimators relative to repeated cross-sectional (RCS) designs, they are often impractical. Methods: We describe the DISC (Different Individuals, Same Clusters) design, a sampling scheme that improves the precision of estimators in these settings. The DISC…

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Uniform inference for kernel instrumental variable regression

核工具变量回归的一致推断

Instrumental variable regression is a foundational tool for causal analysis across the social and biomedical sciences. Recent advances use kernel methods to estimate nonparametric causal relationships, with general data types, while retaining a simple closed-form expression. Empirical researchers ultimately need reliable inference on causal estimates; however, uniform confidence sets for the method remain unavailable. To fill this gap, we develop valid and sharp confidence…

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Discrete Chi-Square Method discovers solar forcing in El Niño time series: The Pacific Ocean as a bolometer measuring the solar dynamo light curve in real-time

离散卡方方法与厄尔尼诺时间序列中的太阳强迫:太平洋辐射计解释

Discrete Chi-square Method (DCM) can detect multiple signals superimposed on an arbitrary trend. DCM's backbone is Gauss-Markov theorem that Least Squares (LS) is the best unbiased estimator for linear regression models. DCM is robust because it computes numerous linear model LS fits. Discrete Fourier Transform and other frequency-domain methods have many application limitations. None of those limitations constrains DCM. Fisher-test provides signal significances and…

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Randomization Tests in Randomized Saturation Designs

随机饱和度设计中的随机化检验

Randomized saturation designs are widely used to study spillover effects in clustered populations. In these designs, clusters are first assigned to treatment saturation levels, and units are then randomized within clusters according to the assigned saturation. This paper develops randomization tests for such experiments under several null hypotheses that arise naturally in spillover analysis. For a fixed pair of saturation levels, we first study two individual-level…

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The Granularity Paradox: How Temporal Disaggregation Inflates In-Sample Fit and Compounds Out-of-Sample Error

时间粒度悖论:细化时间如何提高样本内拟合并累积样本外误差

This paper explores the "Granularity Paradox" in time-series forecasting, wherein finer temporal disaggregation (e.g., Monthly to Weekly/Daily) improves in-sample diagnostics and dataset size (N), but degrades out-of-sample accuracy due to recursive error compounding over longer horizons (H). Conversely, coarse aggregation (Annual) eliminates recursive error propagation but reduces data available to estimators. We formalize this trade-off and benchmark 10 models - spanning…

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Minimum Density Power Divergence Estimation for the Gamma Distribution with Applications to Robust Rainfall Modeling

伽马分布的最小密度幂散度估计及其在稳健降雨建模中的应用

Statistical modeling of rainfall amounts is of considerable importance in meteorology, hydrology, and agriculture. The gamma distribution remains one of the most popular choices for modeling rainfall data due to its flexibility and ability to capture the skewness of rainfall observations. Rainfall datasets often contain atypical observations due to measurement errors and extreme weather events, making maximum likelihood estimation (MLE) highly sensitive to contamination. In…

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Two-way Clustering Robust Variance Estimator in Quantile Regression Models

分位数回归模型中的双向聚类稳健方差估计

We study inference for linear quantile regression with two-way clustered data. Using a separately exchangeable array framework and a projection decomposition of the quantile score, we characterize regime-dependent convergence rates and establish a self-normalized Gaussian approximation. We propose a two-way cluster-robust sandwich variance estimator with a kernel-based density ``bread'' and a projection-matched ``meat'', and prove consistency and validity of inference in…

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Targeted Data Fusion for Region-Specific Survival Effects in the AMP HIV Prevention Trials

AMP 艾滋病预防试验中地区特异性生存效应的定向数据融合

The Antibody Mediated Prevention (AMP) trials opened a new scientific frontier by showing that passively administered monoclonal broadly neutralizing antibodies (bnAbs) could prevent HIV-1 acquisition. Conducted across multiple geographic regions, including the United States, Brazil, Peru, Switzerland, and sub-Saharan Africa, the AMP trials revealed substantial regional heterogeneity in treatment efficacy. These differences, together with privacy and regulatory limits on…

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Targeted Highly Adaptive Lasso Minimum Loss Estimation of Target Functions

目标函数的目标化高度自适应Lasso最小损失估计

We propose a Targeted Highly Adaptive Lasso for estimation of non-pathwise differentiable functional parameters such as the dose-response curve (DRC) for continuous exposure. We assume the target function lies in the $k$-th order smoothness class used to define the $k$-th order Highly Adaptive Lasso (HAL), which can be well approximated by linear spans of $k$-th order spline basis functions. We construct a projection of the true target function onto a large finite…

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Cross-Fitted Survey-Weighted TMLE with Design-Based Variance for Causal Machine Learning

具有设计型方差的交叉拟合调查加权 TMLE

Cross-fitting is not a refinement of survey-weighted causal machine learning but, once the nuisances are flexible, what restores valid inference. We study the population average treatment effect under a stratified multistage design, estimated by a survey-aware targeted maximum likelihood estimator (TMLE) whose variance is obtained by Taylor-series linearization of the influence function, treating the primary sampling unit as the replication unit. Our central result is that…

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Experimental Design When N Equals One

样本个体数为一时的实验设计

N-of-1 trials, or time-series experiments, are widely used in clinical research and online platforms. Yet the theoretically optimal design for estimating many treatment effects remains unclear. We propose a simple Markovian framework for experimental design in which the treatment assignment process is governed by possibly time-varying transition matrices. This formulation encompasses many existing N-of-1 designs and provides a principled way to control temporal dependence in…

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A Pseudo Panel Difference-in-Differences (DiD) Analysis of Online Shopping Behavior in the Puget Sound Regional Council (PSRC) Region

普吉特海湾地区在线购物行为的伪面板双重差分分析

Online shopping is a growing trend, particularly following the COVID-19 lock-downs enacted by many cities. Understanding these trends requires robust panel dat methods. However, panel data (i.e., with repeated measurements of the same observational units) are often unavailable. In this study, we use a propensity score weighting (PSW) approach to adjust repeated cross-sectional travel diary surveys collected in the Puget Sound Regional Council (PSRC) region. The most common…

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What is the Causal Effect of a Conversation? Estimands and Inference in AI Mediated Conversations

对话的因果效应是什么?AI 中介对话的目标量与推断

Political scientists increasingly use conversations as treatments. Sometimes these conversations are conducted by humans, but often and increasingly they will be conducted by generative artificial intelligence (AI). AI makes it possible to scale treatments that are responsive, and rich in real-world relevance. But this same interactivity creates specific challenges for causal inference. A respondent may be randomly assigned to a conversational condition, but the conversation…

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Empirical Bayes for correlated Gaussian sequence model

相关高斯序列模型中的经验贝叶斯方法

Empirical Bayes methods are among the most widely used statistical methods for large-scale inference. A central paradigm is the NPMLE, whose theoretical guarantees are by now well understood for the independent Gaussian sequence model. In this paper, we study empirical Bayes estimation from dependent observations in the Gaussian sequence model. We show that the maximum Composite Marginal Likelihood (CML) estimator, which ignores all correlations in the likelihood, converges…

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Dynamic Heterogeneous Distribution Regression Panel Models, with an Application to Labor Income Processes

动态异质分布回归面板模型及劳动收入应用

We introduce a dynamic distribution regression panel data model with heterogeneous coefficients across units. The objects of primary interest are functionals of these coefficients, including predicted one-step-ahead and stationary cross-sectional distributions of the outcome variable. Coefficients and their functionals are estimated via fixed effect methods. We investigate how these functionals vary in response to counterfactual changes in initial conditions or covariate…

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Is Productivity Advantage of Cities Really Down To Shift, Dilation, and Truncation?

城市生产率优势能否由平移、伸缩与截断解释?

Firms in denser areas are more productive, owing to agglomeration and selection. To disentangle these channels, Combes et al. (2012, ECTA) assume that total factor productivity (TFP) distributions in denser and less dense areas are identical up to shift, dilation, and truncation. Using Spanish firm-level data and methods robust to noisy TFP estimates, we find that TFP distributions are indeed statistically identical up to these parameters, validating such decompositions.…

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Stochastic Frontier meets Breakdown Frontier

随机前沿模型与失效边界分析

This paper studies sensitivity analysis in stochastic frontier models by developing relaxations of the baseline assumptions imposed on the latent inefficiency and noise components, and characterize bounds for a benchmark technical-efficiency object under such relaxations. We then derive the associated breakdown frontier for conclusions about conditional technical efficiency and illustrate the procedure using a well-known dataset. We show the estimation and inference of the…

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Shrinkage through multiple identifiability

通过多重识别实现收缩估计

We propose an empirical Bayes framework for combining estimators obtained from multiple identification functionals associated with the same estimand. We adaptively pool a collection of asymptotically linear estimators, each of which may target a different parameter because of violations of their identification assumptions. Although all estimators are computed from the same sample and are therefore dependent, we show that a working independence construction preserves…

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CaSPECT: Discovering Causally Homogeneous Subgroups via Directed Spectral Clustering

CaSPECT:用有向谱聚类发现因果同质子群

We propose \textbf{CaSPECT}, a causal spectral clustering framework for discovering causally homogeneous subgroups from observational data. Rather than clustering in covariate space, CaSPECT defines similarity through the topology of a learned directed acyclic graph (DAG); a bootstrap-stabilised PC algorithm recovers the causal skeleton; a novel \emph{Orientation Validation Score} (OVS) combines PC bootstrap evidence with DirectLiNGAM to orient edges robustly; directed edges…

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