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Sylvester’s problem for beta-type distributions 西尔维斯特的β型分布问题
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-06-18 DOI: 10.1016/j.spl.2025.110482
Anna Gusakova, Zakhar Kabluchko
{"title":"Sylvester’s problem for beta-type distributions","authors":"Anna Gusakova,&nbsp;Zakhar Kabluchko","doi":"10.1016/j.spl.2025.110482","DOIUrl":"10.1016/j.spl.2025.110482","url":null,"abstract":"<div><div>Consider <span><math><mrow><mi>d</mi><mo>+</mo><mn>2</mn></mrow></math></span> i.i.d. random points <span><math><mrow><msub><mrow><mi>X</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>d</mi><mo>+</mo><mn>2</mn></mrow></msub></mrow></math></span> in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>. In this note, we compute the probability that their convex hull is a simplex focusing on three specific distributional settings: <ul><li><span>•</span><span><div>[(i)] the distribution of <span><math><msub><mrow><mi>X</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> is multivariate standard normal.</div></span></li><li><span>•</span><span><div>[(ii)] the density of <span><math><msub><mrow><mi>X</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> is proportional to <span><math><msup><mrow><mrow><mo>(</mo><mn>1</mn><mo>−</mo><msup><mrow><mo>‖</mo><mi>x</mi><mo>‖</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow><mrow><mi>β</mi></mrow></msup></math></span> on the unit ball (the beta distribution).</div></span></li><li><span>•</span><span><div>[(iii)] the density of <span><math><msub><mrow><mi>X</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> is proportional to <span><math><msup><mrow><mrow><mo>(</mo><mn>1</mn><mo>+</mo><msup><mrow><mo>‖</mo><mi>x</mi><mo>‖</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow><mrow><mo>−</mo><mi>β</mi></mrow></msup></math></span> (the beta prime distribution).</div></span></li></ul> In the Gaussian case, we show that this probability equals twice the sum of the solid angles of a regular <span><math><mrow><mo>(</mo><mi>d</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-dimensional simplex.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"226 ","pages":"Article 110482"},"PeriodicalIF":0.9,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144320966","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
Uniform Hanson-Wright type deviation inequalities for α-subexponential random vectors α-次指数随机向量的统一Hanson-Wright型偏差不等式
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-06-16 DOI: 10.1016/j.spl.2025.110484
Guozheng Dai, Zhonggen Su
{"title":"Uniform Hanson-Wright type deviation inequalities for α-subexponential random vectors","authors":"Guozheng Dai,&nbsp;Zhonggen Su","doi":"10.1016/j.spl.2025.110484","DOIUrl":"10.1016/j.spl.2025.110484","url":null,"abstract":"<div><div>This paper is devoted to uniform versions of the Hanson-Wright inequality for a random vector with independent centered <span><math><mi>α</mi></math></span>-subexponential entries, <span><math><mrow><mn>0</mn><mo>&lt;</mo><mi>α</mi><mo>≤</mo><mn>1</mn></mrow></math></span>. Our method relies on a combination of two existing results: a decoupling inequality and a comparison of weak and strong moments. As an application, we use the derived inequality to prove the restricted isometry property of partial random circulant matrices generated by standard <span><math><mi>α</mi></math></span>-subexponential random vectors, <span><math><mrow><mn>0</mn><mo>&lt;</mo><mi>α</mi><mo>≤</mo><mn>1</mn></mrow></math></span>.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"226 ","pages":"Article 110484"},"PeriodicalIF":0.9,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144307893","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
Existence of small-order moments for Markov-switching stochastic recurrence equations 马尔可夫切换随机递推方程小阶矩的存在性
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-06-16 DOI: 10.1016/j.spl.2025.110483
Baye Matar Kandji
{"title":"Existence of small-order moments for Markov-switching stochastic recurrence equations","authors":"Baye Matar Kandji","doi":"10.1016/j.spl.2025.110483","DOIUrl":"10.1016/j.spl.2025.110483","url":null,"abstract":"<div><div>In this note, we show that the stationary solution of a stochastic recurrence equation, driven by an independent pair of finite-state space Markov chains and an independent and identically distributed process, admits a small-order moment. We use this property to extend, to the entire stationary parameter space, the consistency and asymptotic normality proofs for a recently introduced Hurdle GARCH model.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"226 ","pages":"Article 110483"},"PeriodicalIF":0.9,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144313273","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
The asymptotic behavior of tail moments for light-tailed risks with Sarmanov dependence structure 具有Sarmanov依赖结构的轻尾风险的尾矩渐近行为
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-06-13 DOI: 10.1016/j.spl.2025.110480
Yan Zhang, Kaiyong Wang
{"title":"The asymptotic behavior of tail moments for light-tailed risks with Sarmanov dependence structure","authors":"Yan Zhang,&nbsp;Kaiyong Wang","doi":"10.1016/j.spl.2025.110480","DOIUrl":"10.1016/j.spl.2025.110480","url":null,"abstract":"<div><div>This paper investigates a risk measure called the tail moment <span><math><mfenced><mrow><mtext>TM</mtext></mrow></mfenced></math></span> and presents asymptotic behavior of TMs. The individual risks of a financial or insurance system have the Sarmanov dependence structure. When the individual risks are convolution equivalent or have Gamma-like distributions, the asymptotic results are derived for TMs. The obtained results extend some existing results of TMs for light-tailed risks.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"226 ","pages":"Article 110480"},"PeriodicalIF":0.9,"publicationDate":"2025-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144291329","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
New results on optimal 2-level orthogonal arrays with repeated rows 最优二能级重复行正交阵列的新结果
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-06-09 DOI: 10.1016/j.spl.2025.110476
Fengzhu Cui, Qiang Gao, Guangzhou Chen
{"title":"New results on optimal 2-level orthogonal arrays with repeated rows","authors":"Fengzhu Cui,&nbsp;Qiang Gao,&nbsp;Guangzhou Chen","doi":"10.1016/j.spl.2025.110476","DOIUrl":"10.1016/j.spl.2025.110476","url":null,"abstract":"<div><div>In this letter, we present two novel constructions of optimal 2-level orthogonal arrays with repeated rows. Specifically, we employ the incidence matrices of balanced incomplete block designs (BIBDs) to derive these new optimal 2-level orthogonal arrays containing repeated rows.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"226 ","pages":"Article 110476"},"PeriodicalIF":0.9,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144271086","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
Partially time-invariant panel data regression 部分时不变面板数据回归
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-06-09 DOI: 10.1016/j.spl.2025.110477
Hervé Cardot , Antonio Musolesi
{"title":"Partially time-invariant panel data regression","authors":"Hervé Cardot ,&nbsp;Antonio Musolesi","doi":"10.1016/j.spl.2025.110477","DOIUrl":"10.1016/j.spl.2025.110477","url":null,"abstract":"<div><div>In panel data analysis, temporal variation in the variable of interest is commonly exploited to eliminate individual-specific effects. However, even when the outcome variable follows a continuous distribution, its temporal variation may equal zero with positive probability, resulting in a mixture distribution characterized by a mass at zero alongside a continuous component. To address this, we propose a mixture model and derive estimators for both the conditional probability of no variation and the expected value of the continuous component, focusing on the partial effects. We establish the asymptotic consistency and normality of these estimators and show that paired bootstrap provides consistent confidence intervals for the expected outcome. Monte Carlo simulations show good finite-sample performance of the estimators and reveal that the zero-inflated phenomenon under study can yield substantially different functional relationships depending on the underlying parameters, often making linear models unreliable.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"226 ","pages":"Article 110477"},"PeriodicalIF":0.9,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144254516","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
Cochran–Mantel–Haeszel stratified-adjusted test for multiple odds ratios Cochran-Mantel-Haeszel多优势比分层校正检验
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-06-07 DOI: 10.1016/j.spl.2025.110464
Asmita Ghoshal, John T. Chen
{"title":"Cochran–Mantel–Haeszel stratified-adjusted test for multiple odds ratios","authors":"Asmita Ghoshal,&nbsp;John T. Chen","doi":"10.1016/j.spl.2025.110464","DOIUrl":"10.1016/j.spl.2025.110464","url":null,"abstract":"<div><div>The Cochran–Mantel–Haeszel test (thereby CMH test) is commonly applied to test whether exposure to a risk factor has significant impact on the clinical outcome. However, studies in medical research often require the identification of several significant risk factors simultaneously. In the literature, one of the ubiquitous approaches that strongly control the familywise error rate for multiple tests is the Holm’s step-down procedure. It elegantly applies the first-degree Bonferroni inequality at each step to make inference decisions. On the other hand, when the number of to-be-tested hypotheses is large, Holm’s procedure unavoidably inherits the conservativeness of the Bonferroni inequality, which makes it almost useless when dealing with large number of populations. In this paper, we propose a sequentially rejective procedure for simultaneous inference on odds ratios. We prove that, when testing multiple odds ratios, the new procedure is uniformly more powerful than the Holm’s procedure. Simulation studies show that the improvement is substantial in some scenarios.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"226 ","pages":"Article 110464"},"PeriodicalIF":0.9,"publicationDate":"2025-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144264042","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 new and flexible class of sharp asymptotic time-uniform confidence sequences 一类新的灵活的尖锐渐近时一致置信序列
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-06-07 DOI: 10.1016/j.spl.2025.110462
Felix Gnettner, Claudia Kirch
{"title":"A new and flexible class of sharp asymptotic time-uniform confidence sequences","authors":"Felix Gnettner,&nbsp;Claudia Kirch","doi":"10.1016/j.spl.2025.110462","DOIUrl":"10.1016/j.spl.2025.110462","url":null,"abstract":"<div><div>Confidence sequences are anytime-valid analogues of classical confidence intervals that do not suffer from multiplicity issues under optional continuation of the data collection. As in classical statistics, asymptotic confidence sequences are a nonparametric tool showing under which high-level assumptions asymptotic coverage is achieved so that they also give a certain robustness guarantee against distributional deviations. In this paper, we propose a new flexible class of confidence sequences yielding sharp asymptotic time-uniform confidence sequences under mild assumptions. Furthermore, we highlight the connection to corresponding sequential testing problems and detail the underlying limit theorem.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"226 ","pages":"Article 110462"},"PeriodicalIF":0.9,"publicationDate":"2025-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144264041","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
Fréchet–Shohat theorem: Stronger modes of convergence for a class of absolutely continuous distributions frsamet - shohat定理：一类绝对连续分布的强收敛模式
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-06-06 DOI: 10.1016/j.spl.2025.110466
Pier Luigi Novi Inverardi, Aldo Tagliani
{"title":"Fréchet–Shohat theorem: Stronger modes of convergence for a class of absolutely continuous distributions","authors":"Pier Luigi Novi Inverardi,&nbsp;Aldo Tagliani","doi":"10.1016/j.spl.2025.110466","DOIUrl":"10.1016/j.spl.2025.110466","url":null,"abstract":"<div><div>Using recent results from information theory, maximum entropy (briefly, MaxEnt) and convergence in entropy of MaxEnt densities, stronger modes of convergence than convergence in distribution are obtained for absolutely continuous distributions. As a first result, an alternative proof of the Fréchet–Shohat theorem is given. Moreover, due to the flexibility of the MaxEnt entropy formalism, the new proof is valid for Hamburger, Stieltjes and Hausdorff moment problems with support <span><math><mi>R</mi></math></span>, <span><math><msup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span>, <span><math><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></math></span>, respectively.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"226 ","pages":"Article 110466"},"PeriodicalIF":0.9,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144264043","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
Maximum likelihood estimator of the shape parameter under simple random sampling and moving extremes ranked set sampling 简单随机抽样和移动极值排序集抽样下形状参数的极大似然估计
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-06-04 DOI: 10.1016/j.spl.2025.110465
Rui Yang, Wangxue Chen
{"title":"Maximum likelihood estimator of the shape parameter under simple random sampling and moving extremes ranked set sampling","authors":"Rui Yang,&nbsp;Wangxue Chen","doi":"10.1016/j.spl.2025.110465","DOIUrl":"10.1016/j.spl.2025.110465","url":null,"abstract":"<div><div>This paper examines the maximum likelihood estimator (MLE) for the shape parameter from the shape family, focusing on both simple random sampling (SRS) and moving extremes ranked set sampling (MERSS). The study establishes the existence and uniqueness of the MLE for several common shape distributions. In order to give more insight into the performance of MERSS with respect to (w.r.t.) SRS, the asymptotic efficiency of the MLE using MERSS w.r.t. that using SRS is computed for the common shape distributions. The findings from the common shape distributions indicate that MERSS provides a more efficient approach for estimating the shape parameter compared to SRS. Additionally, we examine the implications of imperfect ranking.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"226 ","pages":"Article 110465"},"PeriodicalIF":0.9,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144213263","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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