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借助多项式逼近建立高斯经验贝叶斯的尖锐遗憾界AI 解读

A central problem in the theory of empirical Bayes is to control the regret (excess risk) of a learned Bayes rule by the Hellinger distance between the estimated and true marginal densities. In the normal means model, the classical result of Jiang and Zhang (2009) achieves this only after regularizing the Bayes rule and incurs an extraneous cubic logarithmic factor through a delicate recursive argument. This paper introduces a new technique, based on polynomial approximation…

OLS 对样本删除的稳健性：理论分析与启示AI 解读

For learned models to be trustworthy, it is essential to verify their robustness to perturbations in the training data. Classical approaches involve uncertainty quantification via confidence intervals and bootstrap methods. In contrast, recent work proposes a more stringent form of robustness: stability to the removal of any subset of $k$ samples from the training set. In this paper, we present a theoretical study of this criterion for ordinary least squares (OLS). Our…

精化的聚类稳健推断AI 解读

It has become standard for empirical studies to conduct inference robust to cluster dependence and heterogeneity. With a small number of clusters, the normal approximation for the $t$-statistics of regression coefficients may be poor. This paper tackles this problem using a critical value based on the conditional Cramér-Edgeworth expansion for the $t$-statistics. The proposed critical value guarantees third-order refinement, and it does not require resampling because it is a…

数字孪生的因果证伪AI 解读

Digital twins are simulation-based models designed to predict how a real-world process will evolve in response to interventions. This modelling paradigm holds substantial promise in many applications, but rigorous procedures for assessing their accuracy are essential for safety-critical settings. We consider how to assess the accuracy of a digital twin using real-world data. We formulate this as a causal inference problem, which leads to a precise definition of what it means…

协变量平衡的再随机化如何缓解回归调整中的显著性操纵AI 解读

Rerandomization enforces covariate balance across treatment groups in the design stage of experiments. Despite its intuitive appeal, its theoretical justification remains unsatisfying because its benefits of improving efficiency for estimating the average treatment effect diminish if we use regression adjustment in the analysis stage. To strengthen the theory of rerandomization, we show that it mitigates false discoveries resulting from $p$-hacking caused by strategically…

贝叶斯 Dirichlet ARMA 的中心化创新：理论等价与银行资产份额应用AI 解读

We study a minimal change to an observation-driven Bayesian Dirichlet ARMA (B--DARMA) for compositional time series: replace the raw additive log-ratio (ALR) residual in the moving-average block with a centered innovation that subtracts the Dirichlet conditional ALR mean, available in closed form via digamma identities. We prove a recursion-level first-order equivalence (in $1/φ$) between the centered specification and a digamma-link DARMA at fixed parameters, under explicit…

自适应实验的连续时间渐近表示AI 解读

This article develops a continuous-time asymptotic framework for analyzing adaptive experiments -- settings in which data collection and treatment assignment evolve dynamically in response to incoming information. A key challenge in analyzing fully adaptive experiments, where the assignment policy is updated after each observation, is that the sequence of policy rules often lack a well-defined asymptotic limit. To address this, we focus instead on the empirical allocation…

库存控制中的损失函数AI 解读

In this paper, we provide analytic expressions for the first-order loss function, the complementary loss function and the second-order loss function for several probability distributions. These loss functions are important functions in inventory optimization and other quantitative fields. For several reasons, which will become apparent throughout this paper, the implementation of these loss functions prefers the use of an analytic expression, only using standard probability…

拟可测空间：概率论的一种便利基础AI 解读

We introduce the categories of quasi-measurable spaces, mild generalizations of quasi-Borel spaces that allow for general sample spaces and less restrictive random variables. Each such category is complete, cocomplete, cartesian closed and, as we show, even locally cartesian closed, a quasitopos and a Heyting category, and so models an extensional dependent type theory with a typed intuitionistic first-order logic. We put one probability monad in the foreground, the…

因果稳定性选择AI 解读

Identifying covariates that modify treatment effects is a central problem in causal inference. Yet existing data-adaptive procedures do not provide finite-sample control over the expected number of false discoveries, risking spurious findings that fail to replicate. We introduce causal stability selection, an algorithm that combines cross-fitted estimation of conditional average treatment effects with integrated path stability selection. The method accommodates arbitrary…

远程照护对住院时长影响的计量分析AI 解读

In this paper, we develop a theoretical model that links the demand for telecare to the length of stay in hospital and formulate three models that can be used to derive the treatment effect by making various assumptions about the probability distribution of the outcome measure. We then fit the models to data and estimate them using a strategy that controls for the effects of confounding variables and unobservable factors, and compare the treatment effects with that of the…

网络干扰下的因果推断AI 解读

We review recent advances in causal inference under interference, drawing on a complex and diverse body of work ranging from causal inference, network science, the health sciences, economics, and the social sciences. Interference in connected populations implies that the treatment assignments of units can affect the outcomes of other units directly (via spillover) and indirectly (via contagion). Examples include public health interventions, economic and financial…

意大利北部PM10评估的三种分布方法AI 解读

We propose three spatial methods for estimating the full probability distribution of PM10 concentrations, with the ultimate goal of assessing air quality in Northern Italy. Moving beyond spatial averages and simple indicators, we adopt a distributional perspective to capture the complex variability of pollutant concentrations across space. The first proposed approach predicts class-based compositions via Fixed Rank Kriging; the second estimates multiple, non-crossing…

基于核岭回归的条件平均处理效应迁移学习AI 解读

The proliferation of data has sparked significant interest in leveraging findings from one study to estimate treatment effects in a different target population without direct outcome observations. However, the transfer learning process is frequently hindered by substantial covariate shift and limited overlap between (i) the source and target populations, as well as (ii) the treatment and control groups within the source. We propose a novel method for overlap-adaptive…

连接预测与归因：利用同化因果推断识别前向与后向因果影响范围AI 解读

Causal inference identifies cause-and-effect relationships between variables. While traditional approaches rely on data to reveal causal links, a recently developed method, assimilative causal inference (ACI), integrates observations with dynamical models. It utilizes Bayesian data assimilation to trace causes back from observed effects by quantifying the reduction in uncertainty. ACI advances the detection of instantaneous causal relationships and the intermittent reversal…

波动率推断的稳健化高斯拟似然方法AI 解读

We consider statistical inference for a class of continuous semimartingale regression models based on high-frequency observations subject to contamination by finite-activity jumps and spike noise. By employing density-power weighting and Hölder-inequality-based normalization, we propose easy-to-implement, robustified versions of the conventional Gaussian quasi-maximum-likelihood estimator that require only a single tuning parameter. We prove their asymptotic mixed normality…

Hurst 指数小于四分之三时混合分数布朗运动的局部渐近正态性AI 解读

This paper establishes the Local Asymptotic Normality (LAN) property for the mixed fractional Brownian motion under high-frequency observations with Hurst index $H \in (0, 3/4)$. The simultaneous estimation of the volatility and the Hurst index encounters a degeneracy problem in the Fisher information matrix.

稀疏双边互动模型中的互补性AI 解读

This paper studies complementarities in two-sided interaction models when only a sparse subset of potential matches is realized. I introduce the Tukey model, adding one complementarity parameter to two-way fixed effects. Variation within a four-cycle in the observed matching network identifies this parameter, while connectedness permits identification of agent productivities. I propose a cycle-based estimator that avoids estimating latent productivities. The estimator is…

观察数据因果推断中的最优传输入门AI 解读

The theory of optimal transportation has developed into a powerful and elegant framework for comparing probability distributions, with wide-ranging applications in all areas of science. The fundamental idea of analyzing probabilities by comparing their underlying state space naturally aligns with the core idea of causal inference, where understanding and quantifying counterfactual states is paramount. Despite this intuitive connection, explicit research at the intersection…