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A completion of counterexamples to the classical central limit theorem for triplewise independent and identically distributed random variables 三独立同分布随机变量经典中心极限定理的反例完成

IF 0.7 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters

Pub Date : 2025-07-25 DOI: 10.1016/j.spl.2025.110508

Martin Raič

By the Lindeberg–Lévy central limit theorem, standardized partial sums of a sequence of mutually independent and identically distributed random variables converge in law to the standard normal distribution. It is known that mutual independence cannot be relaxed to pairwise independence, nor even to triplewise independence. Counterexamples have been constructed for most marginal distributions: a recent construction works under a condition which excludes certain probability distributions with atomic parts, in particular almost all distributions on a fixed finite set. In the present paper, we show that this condition can be lifted: for any probability distribution

F

on the real line, which has finite variance and is not concentrated in a single point, there exists a sequence of triplewise independent random variables with distribution

F

, such that its standardized partial sums converge in law to a distribution which is not normal. There is also scope for extension to

k

-tuplewise independence.

根据lindeberg - lsamvy中心极限定理，一组相互独立且同分布的随机变量序列的标准化部分和规律地收敛于标准正态分布。众所周知，相互独立不能简化为两两独立，甚至不能简化为三倍独立。对于大多数的边际分布已经构造了反例：最近的一个工程在排除某些原子部分的概率分布的条件下进行，特别是在一个固定的有限集合上几乎所有的分布。在本文中，我们证明了这一条件可以被解除：对于实线上任何方差有限且不集中于单点的概率分布F，存在一个分布为F的三重独立随机变量序列，使得它的标准化部分和规律收敛于一个非正态分布。也有扩展到k元独立性的范围。

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引用次数: 0

Nested nearly orthogonal Latin hypercube designs for many design columns 许多设计列的嵌套近正交拉丁超立方体设计

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters

Pub Date : 2025-07-17 DOI: 10.1016/j.spl.2025.110503

Xinxin Xia , Yishan Zhou , Zijian Han

Nested Latin hypercube designs are widely employed for conducting multiple computer experiments with varying levels of fidelity. In the context of polynomial function models, achieving orthogonality is particularly important, as it enables uncorrelated estimation of linear effects under a first-order model. Therefore, maintaining low inter-factor correlation is a highly desirable property in design construction. In this paper, we propose a novel method for constructing nested nearly orthogonal Latin hypercube designs with flexible design columns and low inter-factor correlations. Comparative studies with existing nested Latin hypercube designs demonstrate that the proposed designs achieve lower inter-factor correlations and require fewer runs, making them more efficient and cost-effective for practical applications.

嵌套拉丁超立方体设计被广泛用于进行具有不同保真度的多个计算机实验。在多项式函数模型的背景下，实现正交性尤为重要，因为它可以在一阶模型下对线性效应进行不相关估计。因此，在设计施工中，保持低的因素间相关性是一个非常理想的特性。本文提出了一种构造具有柔性设计列和低因子间相关性的嵌套近正交拉丁超立方体设计的新方法。与现有嵌套拉丁超立方体设计的对比研究表明，所提出的设计实现了更低的因子间相关性，所需的运行次数更少，使其在实际应用中更高效、更具成本效益。

引用次数: 0

On weak convergence of Gaussian conditional distributions 高斯条件分布的弱收敛性

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters

Pub Date : 2025-07-17 DOI: 10.1016/j.spl.2025.110497

Sarah Lumpp , Mathias Drton

Weak convergence of joint distributions generally does not imply convergence of conditional distributions. In particular, conditional distributions need not converge when joint Gaussian distributions converge to a singular Gaussian limit. Algebraically, this is due to the fact that at singular covariance matrices, Schur complements are not continuous functions of the matrix entries. Our results lay out special conditions under which convergence of Gaussian conditional distributions nevertheless occurs, and we exemplify how this allows one to reason about conditional independence in a new class of graphical models.

联合分布的弱收敛性一般并不意味着条件分布的收敛性。特别地，当联合高斯分布收敛于奇异高斯极限时，条件分布不必收敛。在代数上，这是由于在奇异协方差矩阵中，舒尔补不是矩阵项的连续函数。我们的结果列出了高斯条件分布收敛的特殊条件，我们举例说明了这如何允许人们在一类新的图形模型中推理条件独立性。

引用次数: 0

Ergodicity of the stochastic Landau–Lifshitz–Bloch equation with multiplicative and additive noise 具有乘性和加性噪声的随机Landau-Lifshitz-Bloch方程的遍历性

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters

Pub Date : 2025-07-15 DOI: 10.1016/j.spl.2025.110502

Mingli Hong , Zhaoyang Qiu

We study the ergodicity in

H^{1} (D)

of stochastic Landau–Lifshitz–Bloch equation evolving in either smooth bounded domains or unbounded domains, perturbed by both linear multiplicative and additive noises. Such noise is consistent with the fluctuation–dissipation theorem, which can be used to deduce a Boltzmann distribution valid for the full range of temperatures. We find that an exponential moment could be established in regularity space even for the multiplicative noise case. Then, based on it, we prove the exponential ergodicity.

研究了在光滑有界域和无界域上演化的随机Landau-Lifshitz-Bloch方程的H1(D)遍历性。这种噪声与涨落耗散定理是一致的，它可以用来推导出对整个温度范围有效的玻尔兹曼分布。我们发现，即使对于乘性噪声情况，指数矩也可以在正则空间中建立。然后在此基础上证明了指数遍历性。

引用次数: 0

Asymptotics for the ruin probability of a bidimensional renewal risk model with dependent main claims and delayed claims 具有依赖主索赔和延迟索赔的二维续期风险模型破产概率的渐近性

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters

Pub Date : 2025-07-12 DOI: 10.1016/j.spl.2025.110501

Yiqiao Jia, Mingyu Jiang, Dongya Cheng

This paper considers a bidimensional renewal risk model incorporating the dependent main claims and delayed claims, where both the main claims and delayed claims are long-tailed and dominatedly-varying-tailed. It is assumed that both the main claim pairs and the corresponding delayed claim pairs follow the strongly asymptotic independence structure. For this model, a precise asymptotic formula for the finite-time ruin probability is established when the initial surpluses tend to infinity, thereby extending some recent findings in the literature.

本文考虑了包含从属主索赔和延期索赔的二维续展风险模型，其中主索赔和延期索赔都是长尾和显性变尾的。假设主索赔对和相应的延迟索赔对都遵循强渐近独立结构。对于该模型，建立了初始盈余趋于无穷时有限时间破产概率的精确渐近公式，从而推广了文献中的一些最新发现。

引用次数: 0

Distorted expectiles risk measure and LP formulation 扭曲预期物的风险度量与LP的制定

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters

Pub Date : 2025-07-11 DOI: 10.1016/j.spl.2025.110496

Sally Giuseppe Arcidiacono, Damiano Rossello

Given a concave distortion function, we provide a dual representation of the expectiles based on rank-dependent expected utility theory. With possible application to portfolio management in mind, we also derive an LP formulation of the related optimization problem.

给定一个凹畸变函数，我们基于秩相关期望效用理论给出了期望的对偶表示。考虑到可能应用于投资组合管理，我们还推导出相关优化问题的LP公式。

引用次数: 0

Normal approximations for sequences with the property of strong N-demimartingale differences 具有强n -二分差性质的序列的正态逼近

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters

Pub Date : 2025-07-09 DOI: 10.1016/j.spl.2025.110498

Xiaomei Zhang , Jingjun Guo

We consider a class of dependent random variable sequences with the property of strong

N

-demimartingale differences and provide examples to illustrate certain characteristics of these sequences. An upper bound is established for Zolotarev ideal metric between this class of sequences and a normal random variable, thereby leading to the derivation of a central limit theorem for such dependent structure. Additionally, we present numerical analyses to support our findings.

考虑了一类具有强n -二分差性质的相关随机变量序列，并举例说明了这些序列的某些特征。建立了这类序列与正态随机变量之间的Zolotarev理想度量的上界，从而导出了这类相关结构的中心极限定理。此外，我们提出了数值分析来支持我们的发现。

引用次数: 0

Regularity properties of the solution to a stochastic heat equation driven by a bifractional Brownian motion on S2 S2上双分数布朗运动驱动的随机热方程解的正则性

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters

Pub Date : 2025-07-09 DOI: 10.1016/j.spl.2025.110500

Qingbo Wang, Zhenlong Chen

This paper investigates the linear stochastic heat equation on the unit sphere

S^{2}

driven by an infinite dimensional bifractional Brownian noise. We prove the existence and uniqueness of the solution and establish the regularity properties of its sample path. Specifically, we examine the properties of strong local nondeterminism and derive the exact uniform modulus for the solution.

研究了由无限维双分数布朗噪声驱动的单位球S2上的线性随机热方程。证明了该解的存在唯一性，建立了其样本路径的正则性。具体地，我们研究了强局部不确定性的性质，并导出了解的精确一致模。

引用次数: 0

L2-norm posterior contraction in Gaussian models with unknown variance 方差未知的高斯模型l2范数后验收缩

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters

Pub Date : 2025-07-08 DOI: 10.1016/j.spl.2025.110495

Seonghyun Jeong

The testing-based approach is a fundamental tool for establishing posterior contraction rates. Although the Hellinger metric is attractive owing to the existence of a desirable test function, it is not directly applicable in Gaussian models, because translating the Hellinger metric into more intuitive metrics typically requires strong boundedness conditions. When the variance is known, this issue can be addressed by directly constructing a test function relative to the

L_{2}

-metric using the likelihood ratio test. However, when the variance is unknown, existing results are limited and rely on restrictive assumptions. To overcome this limitation, we derive a test function tailored to an unknown variance setting with respect to the

L_{2}

-metric and provide sufficient conditions for posterior contraction based on the testing-based approach. We apply this result to analyze high-dimensional regression and nonparametric regression.

基于测试的方法是建立后宫缩率的基本工具。尽管由于存在理想的测试函数，海灵格度规很有吸引力，但它并不直接适用于高斯模型，因为将海灵格度规转化为更直观的度量通常需要强有界性条件。当方差已知时，这个问题可以通过使用似然比检验直接构造一个相对于l2度量的测试函数来解决。然而，当方差未知时，现有的结果是有限的，并且依赖于限制性的假设。为了克服这一限制，我们推导了一个针对l2度量的未知方差设置的测试函数，并基于基于测试的方法为后验收缩提供了充分的条件。我们将此结果应用于分析高维回归和非参数回归。

引用次数: 0

Iterated tempered stable process 迭代回火稳定过程

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters

Pub Date : 2025-07-08 DOI: 10.1016/j.spl.2025.110499

Ritik Soni , Janusz Gajda , Ashok Kumar Pathak

In this paper, we introduce the iterated tempered stable process (ITSS) by subordinating a tempered

α

-stable subordinator (TSS) with another independent TSS. The proposed model generalizes several important Lévy models studied in Gajda and Wylomańska (2013), Gajda et al., (2019), and Kumar et al., (2017). We derive its distributional properties and explore its connections with fractional calculus. We present sample paths of the ITSS for different parameters and observe perfect agreement between theoretical and empirical Laplace transform estimated from the simulated samples. The tail behavior and the fractional order moments of the ITSS are also discussed. We define the first passage time of the ITSS and study its tail behavior. Additionally, we present a time-changed TSS model and highlight its connection to tempered fractional differential equations.

本文介绍了一个α-稳定的回火子过程（TSS）与另一个独立的TSS从属的迭代回火稳定过程（ITSS）。本文提出的模型概括了Gajda和Wylomańska（2013）、Gajda等人（2019）和Kumar等人（2017）研究过的几个重要的lsamvy模型。我们推导了它的分布性质，并探讨了它与分数阶微积分的联系。我们给出了不同参数下ITSS的样本路径，并观察到由模拟样本估计的理论和经验拉普拉斯变换之间的完美一致性。讨论了ITSS的尾部特性和分数阶矩。我们定义了ITSS的首次通过时间，并研究了它的尾部行为。此外，我们提出了一个时变的TSS模型，并强调了它与缓和分数阶微分方程的联系。

引用次数: 0

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