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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
Statistics & Probability Letters
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
Statistics & Probability Letters
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
Statistics & Probability Letters
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 (k−1)-step transition matrix P(k−1)=Pk−1.
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
Statistics & Probability Letters
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
Statistics & Probability Letters
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
Statistics & Probability Letters
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
On the product of correlated normal random variables and the noncentral chi-square difference distribution 关于相关正态随机变量与非中心卡方差分布的乘积
IF 0.7 4区 数学 Q3 STATISTICS & PROBABILITY
Statistics & Probability Letters
Pub Date : 2025-09-12 DOI: 10.1016/j.spl.2025.110554
Robert E. Gaunt
We represent the product of two correlated normal random variables, and more generally the sum of independent copies of such random variables, as a difference of two independent noncentral chi-square random variables (which we refer to as the noncentral chi-square difference distribution). As a consequence, we obtain, amongst other results, an exact formula for the probability density function of the noncentral chi-square difference distribution, a Stein characterisation of the noncentral chi-square difference distribution, a simple formula for the moments of the sum of independent copies of the product of correlated normal random variables, an exact formula for the probability that such a random variable is negative, and also show that such random variables are self-decomposable and provide a Lévy–Khintchine representation of the characteristic function.
我们表示两个相关的正态随机变量的乘积，更一般地说，是这些随机变量的独立副本的总和，作为两个独立的非中心卡方随机变量的差（我们称之为非中心卡方差分布）。因此，除其他结果外，我们得到了非中心卡方差分布的概率密度函数的精确公式，非中心卡方差分布的斯坦因特征，相关正态随机变量乘积的独立副本之和的矩的简单公式，该随机变量为负的概率的精确公式，并证明了这些随机变量是可自分解的，并给出了特征函数的lcv - khintchine表示。
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引用次数: 0
Parameter estimation of Burgers equations driven by white-colored noise 白噪声驱动下Burgers方程的参数估计
IF 0.7 4区 数学 Q3 STATISTICS & PROBABILITY
Statistics & Probability Letters
Pub Date : 2025-09-11 DOI: 10.1016/j.spl.2025.110553
Yiming Jiang , Yujue Wang , Jie Xue
In this paper, we study the stochastic generalized Burgers equation driven by a white-colored noise with the α-order heat kernel. First we construct a parametric estimator of the drift parameter through temporal quadratic variation of the solution. Then we obtain the consistency and convergence rate of the estimator.
本文研究了具有α阶热核的白色噪声驱动的随机广义Burgers方程。首先通过解的时间二次变分构造漂移参数的参数估计。得到了估计量的相合性和收敛率。
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引用次数: 0
Some general strong laws of large numbers for sequence of measurable operators 可测算子序列的一些一般强数定律
IF 0.7 4区 数学 Q3 STATISTICS & PROBABILITY
Statistics & Probability Letters
Pub Date : 2025-09-11 DOI: 10.1016/j.spl.2025.110551
Nguyen Van Quang , Ali Talebi
In this paper, we establish some general laws of large numbers for sequence of measurable operators such that several known strong law of large numbers (LLN) in von Neumann algebras. One of our main achievements extends the main result of Jajte (2003) in some senses such that Batty’s strong LLN and Łuczak’s result are obtained as special cases. The result is new even in the case of classical random variables.
本文建立了可测算子序列的一些一般大数定律，从而证明了von Neumann代数中已知的几个强大数定律（LLN）。我们的主要成果之一在某种意义上扩展了Jajte（2003）的主要结果，例如Batty的强LLN和Łuczak的结果作为特例得到。即使在经典随机变量的情况下，结果也是新的。
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引用次数: 0
Normal approximation for call function of m-dependent random variables with 2+δ-th moment 具有2+δ-th矩的m相关随机变量调用函数的正态逼近
IF 0.7 4区 数学 Q3 STATISTICS & PROBABILITY
Statistics & Probability Letters
Pub Date : 2025-09-10 DOI: 10.1016/j.spl.2025.110550
Ting Zhang , Lulu Tian , Tianyi Qi
For the call function hk(x)=max{x−k,0} with some fixed k>0, we apply Stein’s method to give the upper bounds of normal approximation under the weaker moment condition, containing both uniform and non uniform situations. Specifically, we discuss a sum of m-dependent and identically distributed random variables with weaker (2+δ)-th moment for some δ∈(0,1). Our results enable the application in call function to possess a broader field with normal approximation techniques.
对于具有固定k>；0的调用函数hk(x)=max{x−k,0}，我们应用Stein方法给出了弱矩条件下正态逼近的上界，包括均匀和非均匀两种情况。具体地说，我们讨论了对某些δ∈(0,1)具有较弱（2+δ）矩的m相关同分布随机变量的和。我们的研究结果使正态近似技术在调用函数中的应用具有更广阔的领域。
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