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Rao-Blackwell 化的 e-变量AI 解读

Summary We show that for any concave utility, the expected utility of an e-variable can only increase after conditioning on a sufficient statistic, echoing the classic Rao-Blackwell theorem. The simplest form of the result has a straightforward proof using Jensen’s inequality, but we prove more sophisticated versions. We provide several applications of this insight, including a derivation of the log-optimal e-variable for testing the variance in a linear regression model.

概率预测中适当损失函数的非对称惩罚AI 解读

Abstract Accurately forecasting the probability distribution of phenomena of interest is a classic and increasingly widespread goal in statistics and decision theory. In comparison to point forecasts, probabilistic forecasts aim to provide a more complete and informative characterization of the target variable. This endeavour is only fruitful, however, if a forecast is ‘close’ to the distribution it attempts to predict. The role of a loss function, also known as a scoring…

任意噪声污染下线性模型的置信区间AI 解读

Summary We study confidence interval construction for linear regression under Huber’s contamination model, where an unknown fraction of noise variables is arbitrarily corrupted. While robust point estimation in this setting is well understood, statistical inference remains challenging, especially because the contamination proportion is not identifiable from the data. We develop a new algorithm that constructs confidence intervals for individual regression coefficients…

高维点过程的正则化谱估计AI 解读

Summary Advances in modern technology have enabled the simultaneous recording of neural spiking activity across large numbers of neurons, which statistically can be represented by a multivariate point process. We characterise the second order structure of this process via the spectral density matrix, a frequency domain equivalent of the covariance matrix. In the context of neuronal analysis, statistics based on the spectral density matrix can be used to infer connectivity in…

两阶段抽样研究的最优两步估计方法AI 解读

Summary Two-phase sampling is commonly adopted for reducing cost and improving estimation efficiency. In many two-phase studies, the outcome and some cheap covariates are observed for a large sample in Phase I, and expensive covariates are obtained for a selected subset of the sample in Phase II. As a result, the analysis of the association between the outcome and covariates faces a missing data problem. Complete-case analysis, which relies solely on the Phase II sample, is…

超越固定截断时点：临床试验中的自适应限制平均生存时间方法AI 解读

Summary Restricted mean survival time offers a compelling nonparametric alternative to hazard ratios for right-censored time-to-event data, particularly when the proportional hazards assumption is violated. By capturing the total event-free time over a specified horizon, it provides an intuitive and clinically meaningful measure of absolute treatment benefit. Nonetheless, selecting the restriction time poses challenges: choosing a small restriction time may overlook…

乘法工具变量模型AI 解读

Summary The instrumental variable (IV) design is a common approach to address hidden confounding bias. For validity, an IV must impact the outcome only through its association with the treatment. In addition, IV identification has required a homogeneity condition such as monotonicity or no unmeasured common effect modifier between the additive effect of the treatment on the outcome, and that of the IV on the treatment. In this work, we introduce the Multiplicative…

预测之外的良性过拟合：普通最小二乘插值估计量AI 解读

Summary Recent advances in deep learning have highlighted the phenomenon of benign overfitting in overparameterized statistical models, sparking significant interest in understanding its foundations. Owing to its simplicity and practical relevance, the ordinary least-squares interpolator has become a key object of study for gaining theoretical insight into this phenomenon. While the properties of ordinary least squares are well understood in classical underparameterized…

测地线双重差分AI 解读

Summary Difference-in-differences (DID) is a widely used quasi-experimental design for causal inference, traditionally applied to scalar or Euclidean outcomes, while extensions to outcomes residing in non-Euclidean spaces remain limited. Existing methods for such outcomes have primarily focused on univariate distributions, leveraging linear operations in the space of quantile functions, but these approaches cannot be directly extended to outcomes in general metric spaces. In…

将预测作为替代结果：人工智能时代重新审视替代结局AI 解读

Abstract We establish a formal connection between the decades-old surrogate outcome model in biostatistics and economics and the emerging field of prediction-powered inference. The connection treats predictions from pre-trained models, prevalent in the age of AI, as cost-effective surrogates for expensive outcomes that are not fully observed. Building on the surrogate outcomes literature, we develop recalibrated prediction-powered inference, a more efficient approach to…

Chatterjee 图相关系数的偏差修正AI 解读

Summary Azadkia & Chatterjee (2021) recently introduced a simple nearest-neighbour graph-based correlation coefficient that consistently detects both independence and functional dependence, in both unconditional and conditional settings. Specifically, it approximates a measure of dependence that equals 0 if and only if the variables are (conditionally) independent, and 1 if and only if they are (conditionally) functionally dependent. However, this nearest-neighbour estimator…

利用中心对称核进行谱密度估计中的短滞后差分AI 解读

Summary Mean-robust estimation of spectral density and long-run variance is crucial for many statistical inference procedures. However, existing methods often degrade when serially dependent data exhibit volatile, time-varying trends, or sudden jumps, particularly in small samples. While differencing and kernel averaging are standard tools for achieving mean robustness and consistency, they are not inherently compatible. Combining them can compromise optimality.…

第一类与第二类错误约束下的最优水印生成AI 解读

Abstract Watermarking has recently emerged as a crucial tool for protecting the intellectual property of generative models and for distinguishing AI-generated content from human-generated data. Despite its practical success, most existing watermarking schemes are empirically driven and lack a theoretical understanding of the fundamental trade-off between detection power and generation fidelity. To address this gap, we formulate watermarking as a statistical hypothesis…

变量缩减后的模型置信集合推断AI 解读

Summary Sparsity in a regression context makes the model itself an object of interest, pointing to a confidence set of models as the appropriate presentation of evidence. A difficulty in areas such as genomics, where the number of candidate variables is vast, arises from the need for preliminary reduction prior to the assessment of models. The present paper considers a resolution using inferential separations fundamental to the Fisherian approach to conditional inference,…

通过显著性水平分配聚合保形预测集合AI 解读

Summary Conformal prediction offers a distribution-free framework for constructing prediction sets with finite-sample coverage. Yet efficiently leveraging multiple nonconformity scores to reduce set sizes remains an open challenge. Instead of selecting a single best score, this work introduces a principled aggregation strategy that intersects multiple conformal prediction sets, with confidence levels allocated optimally to minimize the empirical set size while maintaining…

多成分高斯混合模型下 EM 算法的收敛与最优性AI 解读

Summary Gaussian mixture models are fundamental statistical tools for modelling heterogeneous data. Due to the nonconcavity of the likelihood function, the expectation-maximization (EM) algorithm is widely used for parameter estimation of each Gaussian component. Existing analyses of the EM algorithm’s convergence to the true parameter focus on either the two-component case or multi-component settings with known mixing probabilities and isotropic covariance matrices. In this…

积分概率度量引导的 CUSUM-Net 非参数变点检测AI 解读

Abstract We propose CUSUM-Net, a nonparametric method for changepoint detection based on integral probability metrics and deep neural networks. Our approach learns a critic function by maximizing an aggregate CUSUM objective over candidate changepoints, thereby linking changepoint detection to optimization of two-sample integral probability metrics. The learned critic induces a one-dimensional representation on which changepoints are localized by a classical CUSUM scan.…

一般度量图上的对数高斯 Cox 过程AI 解读

Abstract The modelling of spatial point processes has advanced considerably, yet extending these models to non-Euclidean domains, such as road networks, remains a challenging problem. We propose a novel framework for log-Gaussian Cox processes on general compact metric graphs by leveraging Gaussian Whittle–Matérn fields, which are solutions to fractional-order stochastic differential equations on metric graphs. To achieve computationally efficient likelihood-based inference,…

识别谱尖峰的来源：因子还是混合？AI 解读

Abstract We consider the problem of identifying the pattern of latent variables in high-dimensional linear latent variable models, which can also be interpreted as determining the source of spiked singular values in the data matrix. Specifically, we test whether the latent variables are continuous or categorical, a distinction that is crucial for data interpretation, but challenging in the high-dimensional regime. To address this inference problem, we analyse the asymptotic…

非平衡交叉设计中协方差矩阵的逆AI 解读

SUMMARY This paper addresses a long-standing open problem in crossed random-effects models under unbalanced designs: how to find an analytic expression for the inverse of $ {V} $, the covariance matrix of the observed response. For unbalanced crossed designs, $ {V} $ is dense, and the lack of a closed-form representation for $ {V}^{-1} $ has, until now, made the use of likelihood-based methods computationally challenging and difficult to analyse mathematically. We use the…

一类新的函数型条件自回归模型AI 解读

SUMMARY We introduce a new class of conditional autoregressive models for spatially dependent functional data, formulated through conditional means, given neighbouring functional observations and characterized by a covariance operator and a spatial dependence parameter. Our estimation strategy consists of three components: (i) estimating the covariance operator using conditionally centred data, (ii) estimating the spatial dependence parameter by maximizing the likelihood of…

高维多视图数据协方差结构的推断AI 解读

Summary This article focuses on covariance estimation for multi-view data. Popular approaches rely on factor-analytic decompositions with shared and view-specific latent factors. Posterior computation is conducted via expensive and brittle Markov chain Monte Carlo sampling or variational approximations that underestimate uncertainty and lack theoretical guarantees. Our proposed methodology employs spectral decompositions to estimate and align latent factors that are active…

准贝叶斯经验贝叶斯：泊松复合决策问题的序贯方法AI 解读

SUMMARY The Poisson compound decision problem is a long-standing problem is statistics, for which empirical Bayes methods are commonly used to estimate Poisson means in static or batch settings. We consider this problem in a streaming, or online, framework. Building on a quasi-Bayesian approach based on Newton’s algorithm, we develop a sequential estimate that is easy to evaluate, computationally efficient and has constant per-observation cost as the data accrue. We…

右删失事件时间预测集的双重稳健高效校准AI 解读

Abstract Our objective is to construct well-calibrated prediction sets for a time-to-event outcome subject to right censoring with guaranteed coverage. Inspired by modern conformal inference, our approach avoids the need for a well-specified parametric or semiparametric survival model. Unlike existing conformal methods for survival data, which assume Type-I censoring with fully observed censoring times, we consider the more common right-censoring setting in which only the…