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A new maximum-type test for high-dimensional correlation matrices
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-02-05 DOI: 10.1016/j.spl.2025.110365
Jing Chen , Ming Li , Kaige Zhao , Baisen Liu
{"title":"A new maximum-type test for high-dimensional correlation matrices","authors":"Jing Chen ,&nbsp;Ming Li ,&nbsp;Kaige Zhao ,&nbsp;Baisen Liu","doi":"10.1016/j.spl.2025.110365","DOIUrl":"10.1016/j.spl.2025.110365","url":null,"abstract":"<div><div>The exploration of the structure of high-dimensional correlation matrices has become an increasingly important topic in various fields. This paper aims to develop a novel method for testing the structure of high-dimensional correlation matrices. A new maximum-type test is proposed and the asymptotic distribution is derived, assuming that both the data dimension and the sample size tend towards infinity proportionally. Simulation studies show that our proposed test performs well for the sparse alternatives, dense alternatives, and a mixture of sparse and dense alternatives. Finally, the proposed method is employed to analyze a gene expression dataset.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"220 ","pages":"Article 110365"},"PeriodicalIF":0.9,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143360799","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
Approximately mixing time series
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-02-05 DOI: 10.1016/j.spl.2025.110360
Tim Kutta
{"title":"Approximately mixing time series","authors":"Tim Kutta","doi":"10.1016/j.spl.2025.110360","DOIUrl":"10.1016/j.spl.2025.110360","url":null,"abstract":"<div><div>In this note, we present the new concept of approximate mixing for random variables on metric spaces. Approximate mixing is characterized by two constants <span><math><mrow><mi>ϵ</mi><mo>,</mo><mi>δ</mi><mo>≥</mo><mn>0</mn></mrow></math></span>, where <span><math><mi>ϵ</mi></math></span> is the mixing coefficient and <span><math><mi>δ</mi></math></span> is a slack variable. In the case <span><math><mrow><mi>δ</mi><mo>=</mo><mn>0</mn></mrow></math></span>, approximate mixing reduces to classical <span><math><mi>β</mi></math></span>-mixing. For positive slack, <span><math><mrow><mi>δ</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>, it becomes more general than traditional mixing assumptions, including important time series such as autoregressive processes on Hilbert spaces, that are generally not mixing. We prove that under approximate mixing analogous covariance inequalities hold as in the mixing case. We use these results to prove a central limit theorem for non-stationary time series on Hilbert spaces, which has potential applications in functional data analysis.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"220 ","pages":"Article 110360"},"PeriodicalIF":0.9,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143348646","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
CellMCD+: An improved outlier-resistant cellwise minimum covariance determinant method
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-02-03 DOI: 10.1016/j.spl.2025.110366
Prabhu Babu , Petre Stoica
{"title":"CellMCD+: An improved outlier-resistant cellwise minimum covariance determinant method","authors":"Prabhu Babu ,&nbsp;Petre Stoica","doi":"10.1016/j.spl.2025.110366","DOIUrl":"10.1016/j.spl.2025.110366","url":null,"abstract":"<div><div>In this letter, we revisit the recently proposed cell outlier-resistant method cellMCD (minimum covariance determinant) and derive a version of it called cellMCD+ that has better performance. We illustrate the performance gain of cellMCD+ via numerical simulations in the case of estimating low-rank structured covariance matrices.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"220 ","pages":"Article 110366"},"PeriodicalIF":0.9,"publicationDate":"2025-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143202388","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
Properties of the generalized inverse Gaussian with applications to Monte Carlo simulation and distribution function evaluation
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-01-31 DOI: 10.1016/j.spl.2025.110359
Víctor Peña , Michael Jauch
{"title":"Properties of the generalized inverse Gaussian with applications to Monte Carlo simulation and distribution function evaluation","authors":"Víctor Peña ,&nbsp;Michael Jauch","doi":"10.1016/j.spl.2025.110359","DOIUrl":"10.1016/j.spl.2025.110359","url":null,"abstract":"<div><div>We introduce two mixture representations for the generalized inverse Gaussian (GIG) distribution. One mixture representation expresses the GIG as a continuous mixture of inverse Gaussians. The other reveals a relationship between GIGs. These mixture representations lead to new sampling methods and an exact algorithm for evaluating the distribution function of the GIG for half-integer <span><math><mi>p</mi></math></span>.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"220 ","pages":"Article 110359"},"PeriodicalIF":0.9,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143135861","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
Mean-field fractional BSDEs with locally monotone coefficients
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-01-30 DOI: 10.1016/j.spl.2025.110361
Zongkui Fu , Dandan Fei
{"title":"Mean-field fractional BSDEs with locally monotone coefficients","authors":"Zongkui Fu ,&nbsp;Dandan Fei","doi":"10.1016/j.spl.2025.110361","DOIUrl":"10.1016/j.spl.2025.110361","url":null,"abstract":"<div><div>In this paper, we study mean-field backward stochastic differential equations (BSDEs) driven by fractional Brownian motion with Hurst parameter <span><math><mi>H</mi></math></span> greater than <span><math><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math></span>. With the help of choosing the suitable approximation sequence, we obtain the existence and uniqueness of solution to mean-field fractional BSDEs with locally monotone coefficients.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"220 ","pages":"Article 110361"},"PeriodicalIF":0.9,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143095414","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
Poisson approximation and D(un) condition for extremes of transient random walks in random sceneries
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-01-29 DOI: 10.1016/j.spl.2025.110364
Nicolas Chenavier, Ahmad Darwiche
{"title":"Poisson approximation and D(un) condition for extremes of transient random walks in random sceneries","authors":"Nicolas Chenavier,&nbsp;Ahmad Darwiche","doi":"10.1016/j.spl.2025.110364","DOIUrl":"10.1016/j.spl.2025.110364","url":null,"abstract":"<div><div>Let <span><math><msub><mrow><mrow><mo>(</mo><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mo>≥</mo><mn>0</mn></mrow></msub></math></span> be a transient random walk in the domain of attraction of a stable law and let <span><math><msub><mrow><mrow><mo>(</mo><mi>ξ</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow><mrow><mi>s</mi><mo>∈</mo><mi>Z</mi></mrow></msub></math></span> be a sequence of random variables. Under suitable assumptions, we establish a Poisson approximation result for the point process of exceedances associated with <span><math><msub><mrow><mrow><mo>(</mo><mi>ξ</mi><mrow><mo>(</mo><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></mrow><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mo>≥</mo><mn>0</mn></mrow></msub></math></span> and demonstrate that it satisfies the <span><math><mrow><mi>D</mi><mrow><mo>(</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></mrow></mrow></math></span> condition.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"220 ","pages":"Article 110364"},"PeriodicalIF":0.9,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143095413","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 asymptotic behaviors for branching α-stable process
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-01-29 DOI: 10.1016/j.spl.2025.110362
Nana Luan , Li Wang
{"title":"The asymptotic behaviors for branching α-stable process","authors":"Nana Luan ,&nbsp;Li Wang","doi":"10.1016/j.spl.2025.110362","DOIUrl":"10.1016/j.spl.2025.110362","url":null,"abstract":"<div><div>We consider a branching symmetric <span><math><mi>α</mi></math></span>-stable process in which random split takes place at rate <span><math><mrow><mi>β</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>. We obtain results concerning the long-term behavior of the number of particles surpassing <span><math><msup><mrow><mi>e</mi></mrow><mrow><mi>λ</mi><mi>t</mi></mrow></msup></math></span> at time <span><math><mi>t</mi></math></span> for <span><math><mrow><mi>λ</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>. Additionally, we derive the almost sure asymptotic speed of the rightmost particle as a consequence.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"220 ","pages":"Article 110362"},"PeriodicalIF":0.9,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143095415","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
Logarithmic scale asymptotics for random walks with Weibull-like upper tail distributions
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-01-28 DOI: 10.1016/j.spl.2025.110363
George Stoica , Deli Li
{"title":"Logarithmic scale asymptotics for random walks with Weibull-like upper tail distributions","authors":"George Stoica ,&nbsp;Deli Li","doi":"10.1016/j.spl.2025.110363","DOIUrl":"10.1016/j.spl.2025.110363","url":null,"abstract":"<div><div>We present new asymptotic results in logarithmic scale for random walks with Weibull-like upper tail distributions. The rate of convergence is essentially dictated by the stretched exponential part of the tail distribution therein.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"220 ","pages":"Article 110363"},"PeriodicalIF":0.9,"publicationDate":"2025-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143095412","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 simple consensus model for an increasing population of agents with i.i.d incoming opinions
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-01-25 DOI: 10.1016/j.spl.2024.110345
Ioannis Markou
{"title":"A simple consensus model for an increasing population of agents with i.i.d incoming opinions","authors":"Ioannis Markou","doi":"10.1016/j.spl.2024.110345","DOIUrl":"10.1016/j.spl.2024.110345","url":null,"abstract":"<div><div>In this short note we study what happens in a symmetric opinion model when we send the total interacting population <span><math><mrow><mi>N</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span> to infinity as <span><math><mrow><mi>t</mi><mo>→</mo><mi>∞</mi></mrow></math></span>. We assume that new population enters the system with opinions that are i.i.d random vectors with finite mean and variance. We give sharp conditions on the rate of population growth that is required for convergence to a global consensus in opinions. More particularly, we show that if the total population increases at a rate <span><math><mrow><mi>N</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>∼</mo><msup><mrow><mi>e</mi></mrow><mrow><msup><mrow><mi>t</mi></mrow><mrow><mi>α</mi></mrow></msup></mrow></msup></mrow></math></span>, then <span><math><mrow><mi>α</mi><mo>&lt;</mo><mn>1</mn></mrow></math></span> is necessary and sufficient condition for convergence to the mean of incoming opinions, and the convergence is achieved at an algebraic rate.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"220 ","pages":"Article 110345"},"PeriodicalIF":0.9,"publicationDate":"2025-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143095411","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
Construction of mixed-level designs with minimum discrete discrepancy
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-01-21 DOI: 10.1016/j.spl.2025.110358
Liuping Hu , Kashinath Chatterjee , Jianhui Ning , Hong Qin
{"title":"Construction of mixed-level designs with minimum discrete discrepancy","authors":"Liuping Hu ,&nbsp;Kashinath Chatterjee ,&nbsp;Jianhui Ning ,&nbsp;Hong Qin","doi":"10.1016/j.spl.2025.110358","DOIUrl":"10.1016/j.spl.2025.110358","url":null,"abstract":"<div><div>Mixed-level designs are widely applicable in various practical fields. In this paper, we introduce new methods for constructing mixed-level designs with minimum discrete discrepancy. Utilizing the minimum discrete discrepancy aberration criterion, we establish a valuable analytical connection between the initial design and the resultant design, demonstrating that a high-quality initial design ensures the quality of the resultant design. Additionally, we derive general lower bounds for the discrete discrepancy, which serve as benchmarks for assessing the uniformity of mixed-level designs. Examples are provided to illustrate the effectiveness of our construction methods and the significance of the newly derived lower bounds.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110358"},"PeriodicalIF":0.9,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161085","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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