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Explicit formulae for projectively transformed Cauchy distributions with applications 射影变换柯西分布的显式公式及其应用
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-02-24 DOI: 10.1016/j.spl.2025.110393
Paulo R.S. Mendonça, Ben Lundell
{"title":"Explicit formulae for projectively transformed Cauchy distributions with applications","authors":"Paulo R.S. Mendonça,&nbsp;Ben Lundell","doi":"10.1016/j.spl.2025.110393","DOIUrl":"10.1016/j.spl.2025.110393","url":null,"abstract":"<div><div>Cauchy distributions are characterized as the unique class of continuous distributions invariant to projective transformations, and this result naturally extends to the vector- and matrix-valued cases. We introduce a parameterization of Cauchy distributions that leads to elementary formulae for the parameters of projectively transformed matrix-valued Cauchy random variables, and illustrate an application of this result to the classical computer-vision problem of triangulation.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"222 ","pages":"Article 110393"},"PeriodicalIF":0.9,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143576936","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Efficient sampling in disease surveillance through subpopulations: Sampling canaries in the coal mine 通过亚种群进行疾病监测的有效抽样：煤矿中的金丝雀抽样
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-02-22 DOI: 10.1016/j.spl.2025.110384
Ivo V. Stoepker
{"title":"Efficient sampling in disease surveillance through subpopulations: Sampling canaries in the coal mine","authors":"Ivo V. Stoepker","doi":"10.1016/j.spl.2025.110384","DOIUrl":"10.1016/j.spl.2025.110384","url":null,"abstract":"<div><div>We consider outbreak detection settings of endemic diseases where the population consists of subpopulations available for stratified surveillance. Rather than sampling uniformly across the population, one may elevate effectiveness of detection methodology by optimally choosing a sampling subpopulation. We show (under some assumptions) the relative sampling efficiency between two subpopulations is inversely proportional to the ratio of their baseline disease risks. This implies one can increase sampling efficiency by sampling from the subpopulation with higher baseline disease risk. Our results require careful treatment of power curves of exact binomial tests as a function of their sample size, which are non-monotonic due to the underlying discreteness. A case study of COVID-19 cases in the Netherlands illustrates our theoretical findings.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"222 ","pages":"Article 110384"},"PeriodicalIF":0.9,"publicationDate":"2025-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143552518","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Bahadur representation for sample quantiles of ρ-mixing random variables ρ混合随机变量样本分位数的Bahadur表示
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-02-21 DOI: 10.1016/j.spl.2025.110386
Dagmara Dudek, Anna Kuczmaszewska
{"title":"The Bahadur representation for sample quantiles of ρ-mixing random variables","authors":"Dagmara Dudek,&nbsp;Anna Kuczmaszewska","doi":"10.1016/j.spl.2025.110386","DOIUrl":"10.1016/j.spl.2025.110386","url":null,"abstract":"<div><div>In this paper we investigate the strong consistency and the Bahadur representation of sample quantiles for <span><math><mi>ρ</mi></math></span>-mixing random variables. Moreover, we prove the asymptotic normality and the Berry–Esseen bound of sample quantiles for <span><math><mi>ρ</mi></math></span>-mixing random variables. To illustrate the obtained results some numerical simulations are presented.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"221 ","pages":"Article 110386"},"PeriodicalIF":0.9,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143479553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sufficient conditions for relative aging orders of (n−k+1)-out-of-n systems （n−k+1）-out- n体系相对老化阶的充分条件
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-02-18 DOI: 10.1016/j.spl.2025.110383
M. Kayid, M. Shrahili
{"title":"Sufficient conditions for relative aging orders of (n−k+1)-out-of-n systems","authors":"M. Kayid,&nbsp;M. Shrahili","doi":"10.1016/j.spl.2025.110383","DOIUrl":"10.1016/j.spl.2025.110383","url":null,"abstract":"<div><div>In this paper, we derive sufficient conditions for the preservation of relative aging orders of component lifetimes under the structure of <span><math><mrow><mo>(</mo><mi>n</mi><mo>−</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-out-of-<span><math><mi>n</mi></math></span> systems. Our results strengthen two relative aging properties of <span><math><mrow><mo>(</mo><mi>n</mi><mo>−</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-out-of-<span><math><mi>n</mi></math></span> systems obtained by Misra and Francis (2015).</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"221 ","pages":"Article 110383"},"PeriodicalIF":0.9,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143453710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A short memory condition for infinitely divisible random fields 无限可分随机场的短记忆条件
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-02-17 DOI: 10.1016/j.spl.2025.110385
Vitalii Makogin , Evgeny Spodarev
{"title":"A short memory condition for infinitely divisible random fields","authors":"Vitalii Makogin ,&nbsp;Evgeny Spodarev","doi":"10.1016/j.spl.2025.110385","DOIUrl":"10.1016/j.spl.2025.110385","url":null,"abstract":"<div><div>This small note yields a sufficient condition for the short range dependence of measurable stationary infinitely divisible moving average random fields with <span><math><mi>d</mi></math></span>-dimensional index space. Here, the short/long range dependence concept is borrowed from the paper (Kulik and Spodarev 2021). In the special case of symmetric stable moving averages, our new condition coincides with the one from paper (Makogin et al., 2021).</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"221 ","pages":"Article 110385"},"PeriodicalIF":0.9,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143429184","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Mixingale and physical dependence equality with applications 混合和物理依赖等于应用程序
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-02-17 DOI: 10.1016/j.spl.2025.110380
Jonathan B. Hill
{"title":"Mixingale and physical dependence equality with applications","authors":"Jonathan B. Hill","doi":"10.1016/j.spl.2025.110380","DOIUrl":"10.1016/j.spl.2025.110380","url":null,"abstract":"<div><div>We prove Wu (2005)’s physical dependence and Wu and Min (2005)’s <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-weak dependence properties are asymmetrically equivalent to the adapted mixingale property (each implying the other with possibly different memory decay rates), and identical under geometric memory. We apply the result to two unique cases: (<span><math><mi>i</mi></math></span>) a new Gaussian approximation theory for high dimensional near epoch dependent processes, and (<span><math><mrow><mi>i</mi><mi>i</mi></mrow></math></span>) a new maximal moment inequality for <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-physical dependent arrays when 1 <span><math><mo>&lt;</mo></math></span> <span><math><mi>p</mi></math></span> <span><math><mo>&lt;</mo></math></span> 2.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"221 ","pages":"Article 110380"},"PeriodicalIF":0.9,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143438269","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Necessary and sufficient conditions for the Marcĕnko–Pastur law for sample correlation matrices 样本相关矩阵Marcĕnko-Pastur定律的充分必要条件
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-02-15 DOI: 10.1016/j.spl.2025.110377
Zhaorui Dong, Jianfeng Yao
{"title":"Necessary and sufficient conditions for the Marcĕnko–Pastur law for sample correlation matrices","authors":"Zhaorui Dong,&nbsp;Jianfeng Yao","doi":"10.1016/j.spl.2025.110377","DOIUrl":"10.1016/j.spl.2025.110377","url":null,"abstract":"<div><div>Necessary and sufficient conditions are found for the Marcĕnko–Pastur law to hold for a fairly general class of sample correlation matrices under different moment conditions.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"221 ","pages":"Article 110377"},"PeriodicalIF":0.9,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143465394","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Unbiased estimation of the Gini coefficient 无偏估计基尼系数
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-02-15 DOI: 10.1016/j.spl.2025.110376
Banu Baydil, Victor H. de la Peña, Haolin Zou, Heyuan Yao
{"title":"Unbiased estimation of the Gini coefficient","authors":"Banu Baydil,&nbsp;Victor H. de la Peña,&nbsp;Haolin Zou,&nbsp;Heyuan Yao","doi":"10.1016/j.spl.2025.110376","DOIUrl":"10.1016/j.spl.2025.110376","url":null,"abstract":"<div><div>The Gini coefficient is a fundamental statistical measure of dispersion used widely across multiple fields. The interest in the study of the properties of the Gini coefficient is highlighted by the fact that every year the World Bank ranks the level of income inequality between countries using it. In order to calculate the coefficient, it is common practice to assume a Gamma-distributed set of values when modeling the dispersion of individual incomes in a given population. The asymptotic behavior of the sample Gini coefficient for populations following a Gamma distribution has been well-documented in the literature. However, research on the finite sample behavior has been absent due to the challenge posed by the denominator. This study aims to fill this gap by demonstrating theoretically that the sample Gini coefficient is an unbiased estimator of the population Gini coefficient for a population having Gamma (<span><math><mi>α</mi></math></span>, <span><math><mi>β</mi></math></span>) distribution. Furthermore, our result provides a way to quantify the downward bias due to grouping when the population Gini coefficient is estimated using the sample Gini coefficient of equal-sized groups.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"222 ","pages":"Article 110376"},"PeriodicalIF":0.9,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143529858","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Deviation inequalities for the spectral norm of structured random matrices 结构随机矩阵谱范数的偏差不等式
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-02-13 DOI: 10.1016/j.spl.2025.110378
Guozheng Dai, Zhonggen Su
{"title":"Deviation inequalities for the spectral norm of structured random matrices","authors":"Guozheng Dai,&nbsp;Zhonggen Su","doi":"10.1016/j.spl.2025.110378","DOIUrl":"10.1016/j.spl.2025.110378","url":null,"abstract":"<div><div>We study the deviation inequality for the spectral norm of structured random matrices with non-gaussian entries. In particular, we establish an optimal bound for the <span><math><mi>p</mi></math></span>-th moment of the spectral norm by transfering the spectral norm into the suprema of canonical processes. A crucial ingredient of our proof is a comparison of weak and strong moments. As an application, we show a deviation inequality for the smallest singular value of a rectangular random matrix.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"221 ","pages":"Article 110378"},"PeriodicalIF":0.9,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143422061","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the increments of some extensions of the fractional Brownian motion 分数布朗运动的一些扩展的增量
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-02-13 DOI: 10.1016/j.spl.2025.110381
Charles El-Nouty
{"title":"On the increments of some extensions of the fractional Brownian motion","authors":"Charles El-Nouty","doi":"10.1016/j.spl.2025.110381","DOIUrl":"10.1016/j.spl.2025.110381","url":null,"abstract":"<div><div>Let <span><math><mrow><mo>{</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>H</mi></mrow></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>≥</mo><mn>0</mn><mo>}</mo></mrow></math></span> be a fractional Brownian motion with Hurst index <span><math><mrow><mn>0</mn><mo>&lt;</mo><mi>H</mi><mo>&lt;</mo><mn>1</mn></mrow></math></span>. Given that the process <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>H</mi></mrow></msub></math></span> has stationary increments, a detailed understanding of the characteristics of small, medium, and large increments is essential. This exploration extends to the QHASI class presented as a collection of centered Gaussian processes. This class is mainly characterized by a self-similarity, a quasi-helix and an approximately stationary increments assumptions. However, the analysis of these increments requires a different approach when considering the new extension of <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>H</mi></mrow></msub></math></span> proposed in some previous research. This investigation reveals significant differences in the behavior of increments within this extended framework.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"221 ","pages":"Article 110381"},"PeriodicalIF":0.9,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143421508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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