Statistics & Probability Letters最新文献

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On the robustness of maximum likelihood estimators for the Poisson INAR(1) model Poisson INAR(1)模型的极大似然估计的鲁棒性

IF 0.7 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters

Pub Date : 2026-01-23 DOI: 10.1016/j.spl.2026.110659

Subhankar Chattopadhyay , Sancharee Basak , Atanu Biswas

This article examines the robustness of maximum likelihood estimators in Poisson integer-valued autoregressive processes of order one, which model count time series with autocorrelation and Poisson-distributed innovations. While maximum likelihood estimation is widely used to estimate the autocorrelation parameter

α

and the mean parameter

λ

, its sensitivity to outliers and model deviations remains insufficiently understood. We use influence function theory to quantify the local impact of infinitesimal contamination on the estimators and compute gross error sensitivity to assess worst-case sensitivity. The methodology connects robust statistical ideas with count time series modeling by providing explicit score expressions and estimating Fisher information by simulation under stationarity. Visual diagnostics, including heatmaps, three-dimensional sensitivity surfaces, and summary tables, identify parameter regimes where the estimators become vulnerable to contamination. The study provides practical guidance and diagnostics for applied researchers in the social sciences and epidemiology.

本文研究了一阶泊松整值自回归过程中极大似然估计量的鲁棒性，该过程具有自相关和泊松分布创新。虽然极大似然估计被广泛用于估计自相关参数α和平均参数λ，但其对异常值和模型偏差的敏感性尚不充分了解。我们利用影响函数理论来量化无穷小污染对估计器的局部影响，并计算总误差灵敏度来评估最坏情况灵敏度。该方法通过提供显式分数表达式和在平稳性下通过模拟估计Fisher信息，将稳健的统计思想与计数时间序列建模联系起来。可视化诊断，包括热图、三维灵敏度表面和汇总表，确定估计器容易受到污染的参数制度。该研究为社会科学和流行病学领域的应用研究人员提供了实用的指导和诊断。

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引用次数: 0

Turnpike properties for stochastic linear–quadratic optimal control problems with partial observation 部分观测随机线性二次最优控制问题的收费公路性质

IF 0.7 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters

Pub Date : 2026-01-23 DOI: 10.1016/j.spl.2026.110660

Ruizhe Hu , Huojun Wu

This paper establishes the strong exponential turnpike property for a partially observed stochastic linear–quadratic optimal control problem. We apply an orthogonal decomposition method to decouple the system into filtering and difference processes. Under standard stabilizability and detectability conditions, the convergence of the difference process is proven, leading to the exponential turnpike property with explicitly characterized decay rates. These rates are shown to be governed by the convergence rate between the two decoupled processes.

本文建立了一类部分可观测随机线性二次最优控制问题的强指数收费公路性质。我们采用正交分解方法将系统解耦为滤波和差分过程。在标准的稳定性和可探测性条件下，证明了差分过程的收敛性，得到了具有明确衰减率特征的指数收费公路性质。这些速率是由两个解耦过程之间的收敛速率所控制的。

引用次数: 0

A uniform model selection test for semiparametric models 半参数模型的统一模型选择检验

IF 0.7 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters

Pub Date : 2026-01-20 DOI: 10.1016/j.spl.2026.110658

Francesco Bravo

This paper proposes a new simple test for model selection between two possibly misspecified competing semiparametric models. An important feature of the test is that it controls uniformly its size regardless as to whether the competing models are nested, overlapping or non nested and can be applied to overidentified models with weakly dependent observations.

本文提出了一种新的简单的判别方法，用于判别两个可能错定的竞争半参数模型之间的模型选择。该测试的一个重要特征是，无论竞争模型是嵌套的、重叠的还是非嵌套的，它都能统一地控制其大小，并且可以应用于具有弱依赖观测值的过度识别模型。

引用次数: 0

Exponential inequalities for sampling designs 抽样设计的指数不等式

IF 0.7 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters

Pub Date : 2026-01-20 DOI: 10.1016/j.spl.2026.110654

Guillaume Chauvet , Mathieu Gerber

In this work, we introduce an approach based on the martingale representation of a sampling design and Azuma–Hoeffding’s inequality to derive exponential inequalities for the difference between a Horvitz–Thompson estimator and its expectation. We derive a new exponential inequality for conditionally negatively associated (CNA) sampling designs, which is shown to improve over two existing inequalities that can be used in this context. We establish that Chao’s procedure, Tillé’s elimination procedure and the generalized Midzuno method are CNA sampling designs, and thus obtain an exponential inequality for these three sampling procedures. We show that our approach is useful beyond CNA sampling designs by deriving an exponential inequality for Brewer’s method.

在这项工作中，我们引入了一种基于抽样设计的鞅表示和Azuma-Hoeffding不等式的方法来推导Horvitz-Thompson估计量与其期望之间的差的指数不等式。我们为条件负相关（CNA）抽样设计推导了一个新的指数不等式，它被证明可以改进现有的两个不等式，可以在这种情况下使用。我们建立了Chao方法、till消去方法和广义Midzuno方法是CNA抽样设计，从而得到了这三种抽样方法的指数不等式。通过推导布鲁尔方法的指数不等式，我们证明了我们的方法在CNA抽样设计之外是有用的。

引用次数: 0

When is an Exponentiated Pareto distribution infinitely divisible? 什么时候幂帕累托分布是无限可除的？

IF 0.7 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters

Pub Date : 2026-01-15 DOI: 10.1016/j.spl.2026.110655

Pritam Sarkar , Soumi Thakur Chakraborty , Ayan Pal

We investigate the conditions of infinite divisibility of the Exponentiated Pareto (EP) distribution supported on the entire positive half-line

(0, \infty)

, along with its discrete analogue defined on the set of non-negative integers. The EP distribution is defined via the cumulative distribution function (CDF)

{[F (x)]}^{α}

, where

α > 0

and

F (x) = 1 - {(1 + x)}^{- λ}, x > 0

, is the CDF of Pareto Type II (Lomax) distribution with tail parameter

λ > 0 .

The discrete counterpart is defined as the integer part of a random variable

X

following the EP distribution. The main results assert that both the continuous and discrete versions of the EP distribution are infinitely divisible if

α \in (0, 1] .

A brief discussion of the Lévy process corresponding to the infinitely divisible case for

α \in (0, 1]

is provided along with a real world data illustration.

研究了整条正半线上（0,∞）支持的幂Pareto （EP）分布的无限可除性条件，以及它在非负整数集上定义的离散模拟。EP分布通过累积分布函数（CDF） [F(x)]α来定义，其中α>；0， F(x)=1−(1+x)−λ,x>；0为尾部参数为λ>；0的Pareto Type II （Lomax）分布的CDF。离散对应项定义为随机变量X遵循EP分布的整数部分。主要结果表明，如果α∈(0,1)，EP分布的连续和离散版本都是无限可分的。简要讨论了与α∈(0,1)无限可除情况相对应的lsamvy过程，并给出了一个真实世界的数据说明。

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引用次数: 0

Synchronization of coupled system driven by additive fractional Brownian motion 加性分数布朗运动驱动耦合系统的同步

IF 0.7 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters

Pub Date : 2026-01-15 DOI: 10.1016/j.spl.2026.110657

Meiling Zhao

This paper examines the synchronization of a stochastic coupled system driven by fractional Brownian motion with Hurst parameter

0 < H < \frac{1}{2}

. A key aspect of our analysis is the study of the uniform boundedness of the fractional Ornstein–Uhlenbeck process with a singular parameter, which serves as a crucial tool in determining the convergence rate of synchronization.

本文研究了Hurst参数为0<；H<；12的分数阶布朗运动驱动的随机耦合系统的同步问题。我们分析的一个关键方面是研究具有奇异参数的分数阶Ornstein-Uhlenbeck过程的一致有界性，这是确定同步收敛速度的关键工具。

引用次数: 0

Stochastic stability for linear autoregressive model with Gaussian innovations 高斯创新线性自回归模型的随机稳定性

IF 0.7 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters

Pub Date : 2026-01-15 DOI: 10.1016/j.spl.2026.110656

Ling-Di Wang , Yu Chen , Yong-Hua Mao , Yu-Hui Zhang

Autoregressive model is a basic one among those time series models, whose stochastic stability is crucial, and often a prerequisite, for statistical inference and other applications. As a specific type of time series model, the linear autoregressive model has garnered significant attention due to its simplicity and ease of generalization. In this paper, we present a comprehensive characterization of stability for the linear autoregressive model with Gaussian innovations, including recurrence and transience, the convergence rate in the ergodicity case, and R-stability in the transience case. The linear autoregressive models are fully classified according to their stability, which is entirely determined by their coefficients.

自回归模型是时间序列模型中的一种基本模型，其随机稳定性对统计推断和其他应用至关重要，往往是一个先决条件。线性自回归模型作为时间序列模型的一种特殊类型，因其简单易行、易于泛化而备受关注。本文给出了具有高斯创新的线性自回归模型的稳定性的综合表征，包括递归性和暂态性，遍历情况下的收敛速度，以及暂态情况下的r -稳定性。线性自回归模型根据其稳定性进行完全分类，而稳定性完全由其系数决定。

引用次数: 0

Mathematical research with GPT-5: A Malliavin–Stein experiment GPT-5的数学研究：一个Malliavin-Stein实验

IF 0.7 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters

Pub Date : 2026-01-14 DOI: 10.1016/j.spl.2026.110651

Charles-Philippe Diez , Luís da Maia , Ivan Nourdin

On August 20, 2025, GPT-5,was reported to have solved an open problem in convex optimization. Motivated by this episode, we conducted a controlled experiment in the Malliavin–Stein framework for central limit theorems. Our objective was to assess whether GPT-5 could go beyond known results by extending a qualitative fourth-moment theorem to a quantitative formulation with explicit convergence rates, both in the Gaussian and in the Poisson settings. To the best of our knowledge, the derivation of such quantitative rates had remained an open problem, in the sense that it had never been addressed in the existing literature. The present paper documents this experiment, presents the results obtained, and discusses their broader implications.

2025年8月20日，GPT-5被报道解决了凸优化中的一个开放问题。受此启发，我们在Malliavin-Stein框架下对中心极限定理进行了一个对照实验。我们的目标是评估GPT-5是否可以超越已知的结果，通过将定性的四矩定理扩展到具有显式收敛率的定量公式，在高斯和泊松设置中。据我们所知，这种定量比率的推导一直是一个悬而未决的问题，因为在现有文献中从来没有讨论过这个问题。本文记录了这个实验，给出了得到的结果，并讨论了它们更广泛的含义。

引用次数: 0

The law of thin processes: A law of large numbers for point processes 薄过程定律：点过程的大数定律

IF 0.7 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters

Pub Date : 2026-01-14 DOI: 10.1016/j.spl.2026.110653

Matthew Aldridge

If you take a superposition of

n

IID copies of a point process and thin that by a factor of

1 / n

, then the resulting process tends to a Poisson process as

n \to \infty

. We give a simple proof of this result that highlights its similarity to the law of large numbers and to the law of thin numbers of Harremoës et al.

如果你取一个点过程的n个IID副本的叠加，并将其细化为1/n，那么结果过程趋向于泊松过程，n→∞。我们给出了这个结果的一个简单证明，突出了它与大数定律和Harremoës等人的稀数定律的相似性。

引用次数: 0

Moment inequalities for a class of symmetric distributions 一类对称分布的矩不等式

IF 0.7 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters

Pub Date : 2026-01-14 DOI: 10.1016/j.spl.2026.110652

Weiwei Zhuang, Taizhong Hu

For a class of symmetrically distributed random vectors

(X, Y)

with finite mean, it is shown that

E | X + Y | \geq E | X - Y |

holds, along with its generalizations.

对于一类平均有限的对称分布随机向量（X，Y），证明了E|X+Y|≥E|X−Y|成立，并给出了它的推广。

引用次数: 0

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