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Logarithmic scale asymptotics for random walks with Weibull-like upper tail distributions 具有Weibull-like上尾分布的随机漫步的对数尺度渐近性
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 一个简单的共识模型，用于不断增长的具有传入意见的代理群体
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 离散误差最小的混合水平设计的构造
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
Estimation of the optimal treatment regimes with multiple treatments under proportional hazards model 比例风险模型下多处理方案的最佳处理方案估计
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-01-17 DOI: 10.1016/j.spl.2025.110357
Yuexin Fang , Xiangyong Tan , Qian Li
{"title":"Estimation of the optimal treatment regimes with multiple treatments under proportional hazards model","authors":"Yuexin Fang ,&nbsp;Xiangyong Tan ,&nbsp;Qian Li","doi":"10.1016/j.spl.2025.110357","DOIUrl":"10.1016/j.spl.2025.110357","url":null,"abstract":"<div><div>We propose a novel proportional hazards model that include an unknown baseline covariate effect and the interaction between multiple treatments and covariates on censored survival data. Doubly robust estimating equations constructed by utilizing the A-learning methodology and time-dependent propensity score. The asymptotic properties of the proposed estimators are established under the correct specification of either the baseline effect model or the propensity score model. Extensive simulation studies, along with an application, demonstrate the efficacy of the proposed approach.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110357"},"PeriodicalIF":0.9,"publicationDate":"2025-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161560","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
Sylvester’s problem for random walks and bridges 希尔维斯特的随机漫步和桥梁问题
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-01-12 DOI: 10.1016/j.spl.2024.110349
Hugo Panzo
{"title":"Sylvester’s problem for random walks and bridges","authors":"Hugo Panzo","doi":"10.1016/j.spl.2024.110349","DOIUrl":"10.1016/j.spl.2024.110349","url":null,"abstract":"<div><div>Consider a random walk in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> that starts at the origin and whose increment distribution assigns zero probability to any affine hyperplane. We solve Sylvester’s problem for these random walks by showing that the probability that any <span><math><mrow><mi>d</mi><mo>+</mo><mn>2</mn></mrow></math></span> consecutive steps of the walk are in convex position is equal to <span><math><mrow><mn>1</mn><mo>−</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mrow><mo>(</mo><mi>d</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mo>!</mo></mrow></mfrac></mrow></math></span>. The analogous result also holds for random bridges of length at least <span><math><mrow><mi>d</mi><mo>+</mo><mn>2</mn></mrow></math></span> whose joint increment distribution is exchangeable.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110349"},"PeriodicalIF":0.9,"publicationDate":"2025-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161558","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
Choice of the hypothesis matrix for using the Anova-type-statistic 使用方差统计的假设矩阵的选择
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-01-11 DOI: 10.1016/j.spl.2025.110356
Paavo Sattler , Manuel Rosenbaum
{"title":"Choice of the hypothesis matrix for using the Anova-type-statistic","authors":"Paavo Sattler ,&nbsp;Manuel Rosenbaum","doi":"10.1016/j.spl.2025.110356","DOIUrl":"10.1016/j.spl.2025.110356","url":null,"abstract":"<div><div>Initially developed in <span><span>Brunner et al. (1997)</span></span>, the Anova-type-statistic (ATS) is one of the most used quadratic forms for testing multivariate hypotheses for a variety of different parameter vectors <span><math><mrow><mi>θ</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></mrow></math></span>. Tests based on a version of the ATS are usually preferable over those based on other quadratic forms, like the Wald-type-statistic. However, the same null hypothesis <span><math><mrow><mi>H</mi><mi>θ</mi><mo>=</mo><mi>y</mi></mrow></math></span> can be expressed by various hypothesis matrices <span><math><mrow><mi>H</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>m</mi><mo>×</mo><mi>d</mi></mrow></msup></mrow></math></span> and corresponding vectors <span><math><mrow><mi>y</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>m</mi></mrow></msup></mrow></math></span>, yielding different values of the test statistic. Since this can entail differing test decisions, we investigate under which conditions certain tests using different hypothesis matrices coincide. In this manuscript, we show that for several versions of the Anova-type-statistic, for each hypothesis <span><math><mrow><mi>H</mi><mi>θ</mi><mo>=</mo><mi>y</mi></mrow></math></span> a companion matrix with a minimal number of rows can be constructed, testing the same hypothesis but also always yielding the same test decisions. This can substantially reduce computation time, as demonstrated in several conducted simulations.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110356"},"PeriodicalIF":0.9,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161559","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
Construction of asymmetric resolvable orthogonal arrays 非对称可分辨正交阵列的构造
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-01-09 DOI: 10.1016/j.spl.2025.110355
Xiao Lin, Shanqi Pang
{"title":"Construction of asymmetric resolvable orthogonal arrays","authors":"Xiao Lin,&nbsp;Shanqi Pang","doi":"10.1016/j.spl.2025.110355","DOIUrl":"10.1016/j.spl.2025.110355","url":null,"abstract":"<div><div>Asymmetric resolvable orthogonal arrays have received more and more attention in experimental design, computer experiments, multiple experiments, cross validation, stochastic optimization, and quantum information. However, there are extremely few constructions of asymmetric resolvable orthogonal arrays. This article generalizes the definition of asymmetric resolvable orthogonal arrays and presents some approaches for constructing such arrays.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110355"},"PeriodicalIF":0.9,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161523","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
Some general points for inflation models 通货膨胀模型的一些要点
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-01-07 DOI: 10.1016/j.spl.2024.110346
Dankmar Böhning , Sunisa Junnumtuam
{"title":"Some general points for inflation models","authors":"Dankmar Böhning ,&nbsp;Sunisa Junnumtuam","doi":"10.1016/j.spl.2024.110346","DOIUrl":"10.1016/j.spl.2024.110346","url":null,"abstract":"<div><div>This paper presents a general approach to inflation models with an arbitrary number of inflation points. Using the convex theory of discrete mixture models it achieves some general results including closed form expressions for the estimates of the inflation weights and separability of the likelihood.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110346"},"PeriodicalIF":0.9,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161524","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
Sparse inverse covariance selection with mass-nonlocal priors 质量非局部先验稀疏逆协方差选择
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-01-06 DOI: 10.1016/j.spl.2024.110348
Taiwo Fagbohungbe , Liangliang Zhang , Xuan Cao
{"title":"Sparse inverse covariance selection with mass-nonlocal priors","authors":"Taiwo Fagbohungbe ,&nbsp;Liangliang Zhang ,&nbsp;Xuan Cao","doi":"10.1016/j.spl.2024.110348","DOIUrl":"10.1016/j.spl.2024.110348","url":null,"abstract":"<div><div>To tackle the challenges of understanding complex multivariate relationships in high-dimensional settings, we develop a method for estimating the sparsity pattern of inverse covariance matrices. Our approach employs a generalized likelihood framework for scalable computation, integrating spike and slab priors with nonlocal slab components on the elements of the inverse covariance matrix. We implement the Bayesian model using an entry-wise Gibbs sampler and establish its theoretical consistency in high-dimensional settings under mild conditions. The practical utility of our method is demonstrated through extensive numerical studies and an application to neuropathy data analysis.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110348"},"PeriodicalIF":0.9,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161016","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
Differentially private histogram with valid statistics 具有有效统计的差异私有直方图
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-01-03 DOI: 10.1016/j.spl.2024.110354
Zilong Cao , Shisong Wu , Xuanang Li , Hai Zhang
{"title":"Differentially private histogram with valid statistics","authors":"Zilong Cao ,&nbsp;Shisong Wu ,&nbsp;Xuanang Li ,&nbsp;Hai Zhang","doi":"10.1016/j.spl.2024.110354","DOIUrl":"10.1016/j.spl.2024.110354","url":null,"abstract":"<div><div>Differentially private histograms (DP-Histograms) are integral to data publication and privacy preservation efforts. However, conventional DP-Histograms often fail to preserve valid statistical information and the essential characteristics of the original data. This paper shows the invalidity of variance is the inherent shortcomings in general DP-Histograms, and introduces a novel algorithm called the Differentially Private Histogram with Valid Statistics (VSDPH) to overcome the problem. The VSDPH, grounded in linear programming and bounded Lipschitz distance, efficiently generates DP histograms while preserving the valid statistics of the original data. Our theoretical analysis demonstrates that histograms produced by VSDPH maintain asymptotically valid variance, and we establish an upper bound based on the 1-Wasserstein distance. Through experiments, we validate that VSDPH can accurately hold the statistical characteristics of the original data. This capability brings the resulting histograms closer to the originals.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110354"},"PeriodicalIF":0.9,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161557","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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