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Iterated ergodic theorems and Erdös–Rényi law of large numbers 迭代遍历定理和Erdös-Rényi大数定律
IF 0.7 4区 数学 Q3 STATISTICS & PROBABILITY Pub Date : 2025-09-30 DOI: 10.1016/j.spl.2025.110572
Yuri Kifer
We obtain ergodic theorems and a version of the Erdös–Rènyi law of large numbers for multiple iterated sums and integrals of the form Σ(ν)(t)=0k1<...<kνtξ(k1)ξ(kν), t[0,T] and Σ(ν)(t)=0s1sνtξ(s1)ξ(sν)ds1dsν where {ξ(k)}<k< and {ξ(s)}<s< are stationary vector stochastic processes.
我们得到了多次迭代和积分的遍历定理和Erdös-Rènyi大数定律的一个版本,其形式为Σ(ν)(t)=∑0≤k1<;…<kν≤tξ(k1)⊗⋯⊗ξ(kν), t∈[0,t]和Σ(ν)(t)=∫0≤s1≤⋯≤sν≤tξ(s1)⊗⋯⊗ξ(sν)ds1⋯dsν,其中{ξ(k)}−∞<k<;∞和{ξ(s)}−∞<s<;∞是平稳向量随机过程。
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引用次数: 0
Multiple imputation of censored bivariate event-times via inverse transform and nonparametric Gibbs sampling 基于反变换和非参数Gibbs抽样的截尾双变量事件时间的多次插值
IF 0.7 4区 数学 Q3 STATISTICS & PROBABILITY Pub Date : 2025-09-26 DOI: 10.1016/j.spl.2025.110564
Daniela Angulo, Susan Murray
Bivariate time-to-event data, subject to right censoring, frequently arise in medical research. This paper introduces a novel nonparametric multiple imputation (MI) procedure for analyzing censored bivariate time-to-event data. Our methodology offers a straightforward, easy-to-implement inverse transform MI method that effectively captures the joint distribution of bivariate random variables through the imputation of censored event-times.
医学研究中经常出现经过正确审查的双变量事件时间数据。本文介绍了一种新的非参数多重插值(MI)方法,用于分析截尾双变量时间事件数据。我们的方法提供了一种简单、易于实现的逆变换MI方法,该方法通过截除事件时间的插入有效地捕获二元随机变量的联合分布。
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引用次数: 0
Change-point detection in Vector-Tensor linear model 向量张量线性模型的变点检测
IF 0.7 4区 数学 Q3 STATISTICS & PROBABILITY Pub Date : 2025-09-25 DOI: 10.1016/j.spl.2025.110563
Haiyue Su , Zhiming Xia , Wenyuan Shang , Meili Shi
For high-throughput low-rank data, CANDECOMP/PARAFAC (CP) decomposition is frequently employed to reduce the dimensionality to a manageable level. In this article, we consider a Vector-Tensor linear regression model, where the low-rank structure is expressed through CP decomposition, and the change-point structure is incorporated into the multi-array coefficients. A novel procedure is proposed to jointly detect the change-point and estimate the tensor structure by minimizing the sum of squared residuals. The associated algorithm is developed based on Alternating Least Squares (ALS) algorithm, and is computationally efficient and scalable. Furthermore, we establish the consistency of the change-point estimator under a set of general conditions. Simulations and empirical studies illustrate the validity and effectiveness.
对于高吞吐量低秩数据,经常使用CANDECOMP/PARAFAC (CP)分解将维数降低到可管理的水平。在本文中,我们考虑一个向量张量线性回归模型,其中低秩结构通过CP分解表示,并将变点结构纳入多阵列系数中。提出了一种利用残差平方和最小化来联合检测变点和估计张量结构的新方法。该算法基于交替最小二乘(ALS)算法,具有计算效率高、可扩展性强的特点。进一步,我们在一组一般条件下建立了变点估计量的相合性。仿真和实证研究验证了该方法的有效性。
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引用次数: 0
Double dipping with balanced sampling 双浸均匀取样
IF 0.7 4区 数学 Q3 STATISTICS & PROBABILITY Pub Date : 2025-09-25 DOI: 10.1016/j.spl.2025.110562
Blair Robertson, Chris Price, Marco Reale
Doubly balanced samples from spatial populations have approximate balance on auxiliary variables and spread over spatial coordinates. This article shows that doubly balanced sampling is also efficient on non-spatial populations when we balance on auxiliary variables and spread over the space spanned by them. Numerical results on three example applications show that our extension of doubly balanced sampling works well in practice.
来自空间总体的双平衡样本在辅助变量上具有近似平衡,并且分布在空间坐标上。本文表明,当我们在辅助变量上进行平衡并在它们所跨越的空间上进行扩展时,双平衡抽样对非空间种群也是有效的。三个实例的数值计算结果表明,本文提出的双平衡抽样扩展方法在实际应用中效果良好。
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引用次数: 0
Uniform mean estimation for monotonic processes 单调过程的一致均值估计
IF 0.7 4区 数学 Q3 STATISTICS & PROBABILITY Pub Date : 2025-09-24 DOI: 10.1016/j.spl.2025.110558
Eugenio Clerico , Hamish E. Flynn , Patrick Rebeschini
We consider the problem of deriving uniform confidence bands for the mean of a monotonic stochastic process, such as the cumulative distribution function (CDF) of a random variable, based on a sequence of i.i.d. observations. Our approach leverages the coin-betting framework, and inherits several favourable characteristics of coin-betting methods. In particular, for each point in the domain of the mean function, we obtain anytime-valid confidence intervals that are numerically tight and adapt to the variance of the observations. To derive uniform confidence bands, we employ a continuous union bound that crucially leverages monotonicity. In the case of CDF estimation, we also exploit the fact that the empirical CDF is piece-wise constant to obtain simple confidence bands that can be easily computed. In simulations, we find that our confidence bands for the CDF achieve state-of-the-art performance.
我们考虑了一个单调随机过程均值的均匀置信带问题,如随机变量的累积分布函数(CDF),基于一系列的i.i.d观测值。我们的方法利用投币框架,并继承了投币方法的几个有利特征。特别是,对于平均函数域中的每个点,我们获得了任意时间有效的置信区间,这些置信区间在数值上是紧密的,并且适应于观测值的方差。为了得到一致的置信带,我们使用了一个连续的联合界,它关键地利用了单调性。在CDF估计的情况下,我们还利用经验CDF是分段常数的事实来获得易于计算的简单置信带。在模拟中,我们发现CDF的置信带达到了最先进的性能。
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引用次数: 0
The eschewed sinh-arcsinh t distribution 避开了sinh-arcsinh - t分布
IF 0.7 4区 数学 Q3 STATISTICS & PROBABILITY Pub Date : 2025-09-24 DOI: 10.1016/j.spl.2025.110560
M.C. Jones , Arthur Pewsey
Rosco et al. (2011) introduced and studied the sinh-arcsinh t (SAS-t) distribution. In this article, we introduce a modified version of that distribution which we call the eschewed sinh-arcsinh t (ESAS-t) distribution. The new proposal proves to be somewhat simpler than the former and, on balance, given the pros and cons listed in the article, we now recommend the ESAS-t distribution over the SAS-t distribution as the preferable version of a sinh-arcsinh t distribution.
Rosco et al.(2011)介绍并研究了sinh-arcsinh t (SAS-t)分布。在本文中,我们将介绍该分布的一个修改版本,我们将其称为回避的sinh-arcsinh t (esa -t)分布。事实证明,新提案比前一个提案要简单一些,总的来说,考虑到本文中列出的优点和缺点,我们现在推荐ESAS-t发行版,而不是SAS-t发行版,作为sinh-arcsinh -t发行版的首选版本。
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引用次数: 0
A note on the structure of the filtering recursion for finite HMMs 有限hmm的滤波递归结构注记
IF 0.7 4区 数学 Q3 STATISTICS & PROBABILITY Pub Date : 2025-09-22 DOI: 10.1016/j.spl.2025.110556
Dimitrios Katselis , Boris I. Godoy , Rodrigo Carvajal , Juan C. Agüero
The filter for a finite HMM at time k is expressed in terms of a stochastic matrix Fk. We relate arbitrary pairs of rows in Fk with the corresponding pairs of rows in the underlying (k1)-step transition matrix P(k1)=Pk1.
有限HMM在k时刻的滤波器用随机矩阵Fk表示。我们将Fk中的任意行对与底层(k−1)阶跃变换矩阵P(k−1)=Pk−1中相应的行对联系起来。
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引用次数: 0
Optimal sub-Gaussian variance proxy for truncated Gaussian and exponential random variables 截断高斯和指数随机变量的最优亚高斯方差代理
IF 0.7 4区 数学 Q3 STATISTICS & PROBABILITY Pub Date : 2025-09-22 DOI: 10.1016/j.spl.2025.110555
Mathias Barreto , Olivier Marchal , Julyan Arbel
This paper establishes the optimal sub-Gaussian variance proxy for truncated Gaussian and truncated exponential random variables. The proofs are based initially on reducing each distribution to their standardized versions. Geometrically, for the normal distribution, our argument consists of fitting a parabola to another parabola-looking function, which emerges from its moment generating function. For the exponential case, we show that the optimal variance proxy is the unique solution to a pair of equations and then provide this solution explicitly. Moreover, we demonstrate that truncated Gaussian variables exhibit strict sub-Gaussian behavior if and only if they are symmetric, meaning their truncation is symmetric with respect to the mean. Conversely, truncated exponential variables are shown to never exhibit strict sub-Gaussianity.
本文建立了截断高斯和截断指数随机变量的最优亚高斯方差代理。这些证明最初是基于将每个发行版简化为它们的标准化版本。几何上,对于正态分布,我们的论证包括将抛物线拟合到另一个抛物线状的函数,该函数从其力矩生成函数中出现。对于指数情况,我们证明了最优方差代理是一对方程的唯一解,然后明确地给出了这个解。此外,我们证明截断的高斯变量表现出严格的亚高斯行为当且仅当它们是对称的,这意味着它们的截断相对于均值是对称的。相反,截断的指数变量显示永远不会表现出严格的次高斯性。
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引用次数: 0
Multiple testing in generalized universal inference 广义全称推理中的多重检验
IF 0.7 4区 数学 Q3 STATISTICS & PROBABILITY Pub Date : 2025-09-20 DOI: 10.1016/j.spl.2025.110559
Neil Dey, Ryan Martin, Jonathan P. Williams
Compared to p-values, e-values provably guarantee safe, valid inference. Applications often require consideration of multiple hypotheses simultaneously, and tools for handling such cases using e-values can be found in the relevant literature. Standard e-value constructions, however, require distributional assumptions that may not be justifiable. This short paper demonstrates that, depending on the multiple testing context, the generalized universal inference framework is well-suited for use with the existing e-value merging and adjustment strategies to control frequentist error rates in multiple testing when the quantities of interest are minimizers of risk functions, thereby avoiding the need for certain distributional assumptions. We demonstrate the strong performance of this general approach in a simulation study involving significance testing in quantile regression.
与p值相比,e值可证明地保证安全、有效的推理。应用通常需要同时考虑多个假设,并且可以在相关文献中找到使用e值处理此类情况的工具。然而,标准的e值结构所要求的分布假设可能是不合理的。本文证明,当兴趣量是风险函数的最小值时,根据不同的测试环境,广义通用推理框架非常适合与现有的e值合并和调整策略一起使用,以控制多重测试中的频率错误率,从而避免了对某些分布假设的需要。我们在涉及分位数回归显著性检验的模拟研究中证明了这种一般方法的强大性能。
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引用次数: 0
Communication-efficient distributed robust variable selection for heterogeneous massive data 面向异构海量数据的高效通信分布式鲁棒变量选择
IF 0.7 4区 数学 Q3 STATISTICS & PROBABILITY Pub Date : 2025-09-17 DOI: 10.1016/j.spl.2025.110557
Hang Zou , Yunlu Jiang
We propose a communication-efficient distributed robust variable selection method using discounted exponential regression for massive data. Theoretical properties of the proposed method are demonstrated. Simulation studies and the application to flue gas emission data illustrate the effectiveness of our approach.
针对海量数据,提出了一种基于贴现指数回归的高效通信分布式鲁棒变量选择方法。论证了该方法的理论性质。模拟研究和对烟气排放数据的应用表明了我们方法的有效性。
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引用次数: 0
期刊
Statistics & Probability Letters
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