每日简报

观察性研究中因果推断的样本量与检验力计算AI 解读

This paper investigates the theoretical foundation and develops analytical formulas for sample size and power calculations for causal inference with observational data. By analyzing the variance of an inverse probability weighting estimator of the average treatment effect, we decompose the power calculation into three components: propensity score distribution, potential outcome distribution and their correlation. We show that to determine the minimal sample size of an…

匹配型平均处理效应估计量的高斯与自助法近似AI 解读

We establish Gaussian approximation bounds for covariate and rank-matching-based Average Treatment Effect (ATE) estimators. By analyzing these estimators through the lens of stabilization theory, we employ the Malliavin–Stein method to derive our results. Our bounds precisely quantify the impact of key problem parameters, including the number of matches and treatment balance, on the accuracy of the Gaussian approximation. Additionally, we develop multiplier bootstrap…

高阶图极限函数理论：波动、退化与推断AI 解读

Exchangeable random graphs, which include some of the most widely studied network models, have emerged as the mainstay of statistical network analysis in recent years. Graphons, which are the central objects in graph limit theory, provide a natural way to sample exchangeable random graphs. It is well known that network moments (motif/subgraph counts) identify a graphon (up to an isomorphism); hence, understanding the sampling distribution of subgraph counts in random graphs…

数据增强算法的快速混合：贝叶斯 probit、logit 与 lasso 回归AI 解读

We propose using a modified conductance-based method to study the mixing time of an important class of two-block Gibbs samplers, the data augmentation (DA) algorithm. Using this method, we prove the first non-asymptotic polynomial upper bounds on mixing times of three important DA algorithms: DA algorithms for Bayesian Probit regression (ProbitDA) and Bayesian Logit regression (LogitDA), and Bayesian Lasso Regression (LassoDA). Concretely, for ProbitDA and LogitDA, we…

超越随机缺失与完全随机缺失的估计AI 解读

We study the effects of missingness on the estimation of population parameters. Moving beyond restrictive missing completely at random (MCAR) assumptions, we first formulate a missing data analogue of Huber’s arbitrary ϵ-contamination model. For mean estimation with respect to squared Euclidean error loss, we show that the minimax quantiles decompose as a sum of the corresponding minimax quantiles under a heterogeneous, MCAR assumption and a robust error term, depending on…

高维秩一推断的伪最大似然理论AI 解读

We develop a pseudo-likelihood theory for rank one matrix estimation problems in the high-dimensional limit. We prove a variational principle for the limiting pseudo-maximum likelihood, which also characterizes the performance of the corresponding pseudo-maximum likelihood estimator. We show that this variational principle is universal and depends only on four parameters determined by the corresponding null model. Through this universality, we introduce a notion of…

阈值空间由直线划分的广义多元阈值自回归模型AI 解读

We consider a k-dimensional multiple-regime vector threshold autoregressive model, in which the regime-switching mechanism is governed by a bivariate threshold variable. Specifically, the regimes are induced by a partition of the threshold space by an unknown number of threshold lines. Within each regime, the process follows a specific vector autoregressive (VAR) model. We formulate the model selection and parameter estimation into a minimization problem based on the Minimum…

高度分层实验的估计效率AI 解读

This paper studies the use of highly stratified designs for the efficient estimation of a large class of treatment effect parameters that arise in the analysis of experiments. By a “highly stratified” design, we mean experiments in which units are divided into blocks of a fixed size and a proportion within each block is assigned to a binary treatment uniformly at random. The class of parameters considered are those that can be expressed as the solution to a set of moment…

随机对象的关联度量与独立性检验AI 解读

We develop a unified framework for testing independence and quantifying association between random objects that are located in general metric spaces. Special cases include functional and high-dimensional data as well as networks, covariance matrices and data on Riemannian manifolds, among other metric space-valued data. A key concept is the profile association, a measure based on distance profiles that intrinsically characterize the distributions of random objects in metric…

使用不精确梯度的无偏动量Langevin Monte CarloAI 解读

We present an unbiased method for Bayesian posterior means based on kinetic Langevin dynamics that combines advanced splitting methods with enhanced gradient approximations. Our approach avoids Metropolis correction by coupling Markov chains at different discretization levels in a multilevel Monte Carlo approach. Theoretical analysis demonstrates that our proposed estimator is unbiased, attains finite variance, and satisfies a central limit theorem. It can achieve accuracy…

污染机制下后验采样的隐私保证AI 解读

In recent years, differential privacy has been adopted by tech-companies and governmental agencies as the standard for measuring privacy in algorithms. In this article, we study differential privacy in Bayesian posterior sampling settings. We begin by considering differential privacy in the most common privatisation setting in which Laplace or Gaussian noise is injected into the output. In an effort to achieve better differential privacy, we consider adopting Huber’s…

用 e 值衡量反对交换性与群不变性的证据AI 解读

We study e-values for quantifying evidence against exchangeability and general invariance of a random variable under a compact group. We start by characterizing such e-values, and explaining how they nest traditional group invariance tests as a special case. We show they can be easily designed for an arbitrary test statistic, and computed through Monte Carlo sampling. We prove a result that characterizes optimal e-values for group invariance against optimality targets that…

变量选择的假发现率估计AI 解读

We introduce a generic estimator for the false discovery rate of any model selection procedure, in common statistical modeling settings including the Gaussian linear model, Gaussian graphical model, and model-X setting. We prove that our method has a conservative (nonnegative) bias in finite samples under standard statistical assumptions, and provide a bootstrap method for assessing its standard error. For methods like the Lasso, forward-stepwise regression, and the…

DiPMInd：基于距离剖面的随机对象相互独立性检验AI 解读

This paper develops a novel unified framework for testing mutual independence among random objects residing in possibly different metric spaces. The framework generalizes existing methodologies and introduces new measures of mutual independence, and proposes associated tests that achieve minimax rate optimality and exhibit strong empirical power. The foundation of the proposed tests is the new concept of joint distance profiles, which uniquely characterize the joint law of…

基于分割的非参数 M 估计量的一致估计与推断AI 解读

This paper presents uniform estimation and inference theory for a large class of nonparametric partitioning-based M-estimators. The main theoretical results include: (i) uniform consistency for convex and nonconvex objective functions; (ii) rate-optimal uniform Bahadur representations; (iii) rate-optimal uniform (and mean square) convergence rates; (iv) valid strong approximations and feasible uniform inference methods; and (v) extensions to functional transformations of…

流形上的高阶精确统计推断AI 解读

We present a new framework for statistical inference on Riemannian manifolds that achieves high-order accuracy, addressing the challenges posed by non-Euclidean parameter spaces frequently encountered in modern data science. Our approach leverages a novel and computationally efficient procedure to reach higher-order asymptotic precision. In particular, we develop a bootstrap algorithm on Riemannian manifolds that is both computationally efficient and accurate for hypothesis…

高维混合模型的局部几何：有效谱理论与动力学转变AI 解读

We study the local geometry of empirical risks in high dimensions via the spectral theory of their Hessian and information matrices. We focus on settings where the data, (Yℓ)ℓ=1n∈Rd, are i.i.d. draws of a k-Gaussian mixture model, and the loss depends on the projection of the data into a fixed number of vectors, namely x⊤Y, where x∈Rd×C are the parameters, and C need not equal k. This setting captures a broad class of problems such as classification by one and two-layer…

稀疏与稳健回归中近似消息传递的非渐近分布理论AI 解读

Characterizing the distribution of high-dimensional statistical estimators is a challenging task, due to the breakdown of classical asymptotic theory in high dimension. This paper makes progress towards this by developing non-asymptotic distributional characterizations for approximate message passing (AMP)—a family of iterative algorithms that prove effective as both fast estimators and powerful theoretical machinery—for both sparse and robust regression. Prior AMP theory,…

局部稳健且半参数有效的贝叶斯推断AI 解读

We propose a framework for making Bayesian parametric models robust to local misspecification. Suppose in a baseline parametric model, a parameter of interest has an interpretation in an encompassing semiparametric model. Bayesian and maximum likelihood estimators are generally biased under local misspecification. We propose to augment the baseline likelihood by a multiplicative factor that involves scores for the baseline model, the efficient scores for the encompassing…

空间处理的因果推断AI 解读

Many events and policies (treatments) occur at specific spatial locations, with researchers interested in their effects on nearby units. I approach the spatial treatment setting from an experimental perspective: What ideal experiment would we design to estimate the causal effects of spatial treatments? This perspective motivates a comparison between units near realized treatment locations and units near counterfactual (unrealized) candidate locations, which differs from…

局部投影的双重稳健性与 VAR 推断的隐患AI 解读

We consider impulse response inference in a locally misspecified vector autoregression (VAR) model. The conventional local projection (LP) confidence interval has correct coverage even when the misspecification is so large that it can be detected with probability approaching 1. This result follows from a “double robustness” property analogous to that of popular partially linear regression estimators. By contrast, the conventional VAR confidence interval with…

经济增长与大型企业的崛起AI 解读

I document that the right tail of the firm size distribution systematically thickens with economic development. To rationalize this fact, I develop a parsimonious idea search model in which both aggregate growth and the firm size distribution are endogenously determined. The model features an asymptotic balanced growth path along which Gibrat's law holds at each date, and the right tail of the firm size distribution thickens monotonically toward Zipf's law. The model also…

个性化政策的机制设计：激励运动的实地实验AI 解读

Personalizing policies can theoretically increase their effectiveness. However, personalization is difficult when individual types are unobservable and the preferences of policymakers and individuals are not aligned, which could cause individuals to misreport their type. Mechanism design offers a strategy to overcome this issue: offer an “incentive‐compatible” menu of policy choices designed to induce participants to select the variant intended for their type. Using a field…

高斯过程最大值位置分布函数的连续性AI 解读

Certain extremum estimators have asymptotic distributions that are non‐Gaussian, yet characterizable as the distribution of the arg max of a Gaussian process. This paper presents high‐level sufficient conditions under which such asymptotic distributions admit a continuous distribution function. The plausibility of the sufficient conditions is demonstrated by verifying them in three examples, namely, maximum score estimation, empirical risk minimization, and threshold…