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张量因子模型中Kronecker积结构的检验AI 解读

Abstract We propose a test for the Kronecker product structure of a factor loading matrix implied by a tensor factor model with Tucker decomposition in the common component. By defining a Kronecker product structure set, we determine whether a tensor time series has a Kronecker product structure, equivalent to its ability to decompose the series according to a tensor factor model. Our test is built on analysing and comparing the residuals from fitting a full tensor factor…

二阶无偏贝叶斯估计量的先验构造AI 解读

Summary Asymptotically unbiased priors, introduced by Hartigan (1965), are designed to achieve second-order unbiasedness of Bayes estimators. This paper extends Hartigan’s framework to non-independent-and-identically-distributed models by deriving a system of partial differential equations that characterizes asymptotically unbiased priors. Furthermore, we establish a necessary and sufficient condition for the existence of such priors and propose a simple procedure for…

一般抽样设计下小区域预测的替代均方误差估计与置信区间AI 解读

Abstract Estimating the mean square error of a small area predictor under an informative sampling design is a challenging problem. Existing approaches rely on approximations that have not been justified theoretically. We provide rigorous support for a mean square error estimator that is applicable to an informative sample design. The procedure can be used in combination with predictors of general parameters that may be nonlinear functions of the model response variable. We…

有监督污染检测及其流式细胞术应用AI 解读

Summary The contamination detection problem aims to determine whether a set of observations has been contaminated, i.e., whether it contains points drawn from a distribution different from the reference distribution. Here, we consider a supervised problem, where labelled samples drawn from both the reference distribution and the contamination distribution are available at training time. This problem is motivated by the detection of rare cells in flow cytometry. Compared to…

多元高斯累积分布函数与对偶贝叶斯 probit 模型的边际似然AI 解读

Summary The computation of multivariate Gaussian cumulative distribution functions is a key step in many statistical procedures, often representing a crucial computational bottleneck. Over the past few decades, efficient algorithms have been proposed to address this problem, mainly using Monte Carlo solutions. This work highlights a connection between the multivariate Gaussian cumulative distribution function and the marginal likelihood of a tailored dual Bayesian probit…

网络关联数据的高维因子分析AI 解读

Summary Factor analysis is a statistical tool widely used in many disciplines, such as psychology, economics and sociology. As observations linked by networks become increasingly common, incorporating network structures into factor analysis is an important problem that remains open. This article focuses on high-dimensional factor analysis involving network-connected observations, and we propose a generalized factor model with latent factors that account for both the network…

多重插补数据的重抽样方法AI 解读

Abstract Resampling techniques have become increasingly popular for estimation of uncertainty. However, data are often fraught with missing values that are commonly imputed to facilitate analysis. This article addresses the issue of using resampling methods such as a jackknife or bootstrap in conjunction with imputations that have been sampled stochastically, in the vein of multiple imputation. We derive the theory needed to illustrate two key points regarding the use of…

更稳健的多变量孟德尔随机化方法AI 解读

Summary Multivariable Mendelian randomization uses genetic variants as instrumental variables to infer the direct effects of multiple exposures on an outcome. However, unlike univariable Mendelian randomization, multivariable Mendelian randomization often faces greater challenges with many weak instruments, which can lead to bias not necessarily toward zero and inflation of Type-I errors. In this work, we introduce a new asymptotic regime that allows exposures to have…

逆卡尔曼滤波器AI 解读

Summary We introduce the inverse Kalman filter, which enables exact matrix-vector multiplication between a covariance matrix from a dynamic linear model and any real-valued vector with linear computational cost. We integrate the inverse Kalman filter with the conjugate gradient algorithm, which substantially accelerates the computation of matrix inversion for a general form of covariance matrix, where other approximation approaches may not be directly applicable. We…

利用高维数据增广估计尖峰协方差模型的维度AI 解读

Summary We propose a modified, high-dimensional version of a recent dimension estimation procedure that determines the dimension via the introduction of augmented noise variables into the data. Our asymptotic results show that the proposal is consistent in wide, high-dimensional scenarios, and further shed light on why the original method breaks down when the dimension of either the data or the augmentation becomes too large. Simulations and real data are used to demonstrate…

贝叶斯多元逻辑回归模型中的因子预训练AI 解读

Abstract This article focuses on inference in logistic regression for high-dimensional binary outcomes. A popular approach induces dependence across the outcomes by including latent factors in the linear predictor. Bayesian approaches are useful for characterizing uncertainty in inferring the regression coefficients, factors and loadings, while also incorporating hierarchical and shrinkage structures. However, Markov chain Monte Carlo algorithms for posterior computation…

线性非高斯结构方程模型的拟合优度检验AI 解读

Abstract The field of causal discovery develops model selection methods to infer cause-effect relations among a set of random variables. For this purpose, different modelling assumptions have been proposed to render cause-effect relations identifiable. One prominent assumption is that the joint distribution of the observed variables follows a linear non-Gaussian structural equation model. In this paper, we develop novel goodness-of-fit tests that assess the validity of this…

用于政策学习的半参数工具变量双重差分方法AI 解读

Summary Recently, there has been a surge in methodological development for the difference-in-differences approach to evaluate causal effects. Standard methods in the literature rely on the parallel-trend assumption to identify the average treatment effect on the treated. However, the parallel-trend assumption may be violated in the presence of unmeasured confounding, and the average treatment effect on the treated may not be useful in learning a treatment assignment policy…

删失生存数据的多重校准与普适适应性AI 解读

Summary Traditional statistical and machine learning methods typically assume that the training and test data follow the same distribution. However, this assumption is frequently violated in real-world applications, where the training data in the source domain may underrepresent specific subpopulations in the test data of the target domain. This article addresses target-independent learning under covariate shift, focusing on multicalibration for survival probability and…

非欧随机对象的稳健函数主成分分析AI 解读

Summary Functional data analysis offers a diverse toolkit of statistical methods tailored to analysing samples of real-valued random functions. Recently, samples of time-varying random objects, such as time-varying networks, have been increasingly encountered in data analysis. These data structures represent elements within general metric spaces that lack local or global linear structures, rendering traditional functional data analysis methods inapplicable. Moreover, the…

状态切换整数值自回归模型AI 解读

Time series of counts often display complex dynamic and distributional characteristics. For this reason, we develop a flexible framework combining the integer-valued autoregressive (INAR) model with a latent Markov structure, leading to the hidden Markov model-INAR (HMM-INAR). First, we illustrate conditions for the existence of an ergodic and stationary solution and derive closed-form expressions for the autocorrelation function and its components. Second, we show…

稳健的高维时变系数估计AI 解读

In this article, we develop a novel high-dimensional coefficient estimation procedure based on high-frequency data. Unlike usual high-dimensional regression procedures such as LASSO, we additionally handle the heavy-tailedness of high-frequency observations as well as time variations of coefficient processes. Specifically, we employ the Huber loss and a truncation scheme to handle heavy-tailed observations, while $\ell _{1}$ -regularization is adopted to overcome the curse…

基于核现货波动率估计量的积分波动率泛函估计AI 解读

For a multidimensional Itô semimartingale, we consider the problem of estimating integrated volatility functionals. Jacod and Rosenbaum (2013, The Annals of Statistics 41(3), 1462–1484) studied a plug-in type of estimator based on a Riemann sum approximation of the integrated functional and a spot volatility estimator with a forward uniform kernel. Motivated by recent results that show that spot volatility estimators with general two-sided kernels of unbounded support are…

RLHF 对齐的算法偏差：偏好坍缩与匹配正则化AI 解读

Accurately aligning large language models (LLMs) with human preferences is crucial for informing fair, economically sound, and statistically efficient decision-making processes. However, we argue that the predominant approach for aligning LLMs with human preferences through a reward model—reinforcement learning from human feedback (RLHF)—suffers from an inherent algorithmic bias due to its Kullback–Leibler-based regularization in optimization. In extreme cases, this bias…

混合模型：参数、半参数与新方向AI 解读

Weixin Yao and Sijia Xiang. Boca Raton, FL: Chapman & Hall/CRC Press, 2024, xvii + 379 pp., $130.00(H), ISBN: 978-0-367-48182-7.The mixture modeling framework has become a mainstay in the toolkit o...

整合个体数据与汇总数据的贝叶斯随机效应元分析AI 解读

Meta-analysis using individual participant data (IPD) offers many benefits, including greater analytical flexibility, compared to conventional analyses based on aggregate data (AD). However, it is often hindered by restricted access to IPD. Relying solely on available IPD may introduce “data availability bias,” compromising external validity. Integrating IPD with relevant AD addresses this concern, but existing methods are restrictive, requiring precise knowledge of the…

受多臂老虎机启发的模型不确定性下最优设计AI 解读

An optimal design is usually model-dependent and is sub-optimal if the postulated model is not correctly specified. Furthermore, it is far from ideal even if it is efficient for model selection but has a poor performance for estimating parameters in the selected model. In practice, it is common that a researcher has a list of candidate models at hand and a design has to be found that is efficient for both model discrimination and parameter estimation in the (unknown) “true”…

独立簇数据的随机效应充分降维AI 解读

Sufficient dimension reduction (SDR) is a popular class of regression methods which aim to find a small number of linear combinations of covariates that capture all the information of the responses i.e., a central subspace. The majority of current methods for SDR focus on the setting of independent observations, while the few techniques that have been developed for clustered data assume the linear transformation is identical across clusters. In this article, we introduce…

利用统计推断增强 AI 生成生物医学图像的可信度AI 解读

Generative artificial intelligence (AI) has transformed the biomedical imaging field through image synthesis, addressing challenges of data availability, privacy, and diversity in biomedical research. This paper proposes a novel nonparametric method within the functional data framework to discern significant differences between the mean and covariance functions of original and synthetic biomedical imaging data, thereby enhancing the fidelity and utility of synthetic data.…