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L2-norm posterior contraction in Gaussian models with unknown variance 方差未知的高斯模型l2范数后验收缩
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-07-08 DOI: 10.1016/j.spl.2025.110495
Seonghyun Jeong
{"title":"L2-norm posterior contraction in Gaussian models with unknown variance","authors":"Seonghyun Jeong","doi":"10.1016/j.spl.2025.110495","DOIUrl":"10.1016/j.spl.2025.110495","url":null,"abstract":"<div><div>The testing-based approach is a fundamental tool for establishing posterior contraction rates. Although the Hellinger metric is attractive owing to the existence of a desirable test function, it is not directly applicable in Gaussian models, because translating the Hellinger metric into more intuitive metrics typically requires strong boundedness conditions. When the variance is known, this issue can be addressed by directly constructing a test function relative to the <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-metric using the likelihood ratio test. However, when the variance is unknown, existing results are limited and rely on restrictive assumptions. To overcome this limitation, we derive a test function tailored to an unknown variance setting with respect to the <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-metric and provide sufficient conditions for posterior contraction based on the testing-based approach. We apply this result to analyze high-dimensional regression and nonparametric regression.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"226 ","pages":"Article 110495"},"PeriodicalIF":0.9,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144589278","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
Iterated tempered stable process 迭代回火稳定过程
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-07-08 DOI: 10.1016/j.spl.2025.110499
Ritik Soni , Janusz Gajda , Ashok Kumar Pathak
{"title":"Iterated tempered stable process","authors":"Ritik Soni ,&nbsp;Janusz Gajda ,&nbsp;Ashok Kumar Pathak","doi":"10.1016/j.spl.2025.110499","DOIUrl":"10.1016/j.spl.2025.110499","url":null,"abstract":"<div><div>In this paper, we introduce the iterated tempered stable process (ITSS) by subordinating a tempered <span><math><mi>α</mi></math></span>-stable subordinator (TSS) with another independent TSS. The proposed model generalizes several important Lévy models studied in Gajda and Wylomańska (2013), Gajda et al., (2019), and Kumar et al., (2017). We derive its distributional properties and explore its connections with fractional calculus. We present sample paths of the ITSS for different parameters and observe perfect agreement between theoretical and empirical Laplace transform estimated from the simulated samples. The tail behavior and the fractional order moments of the ITSS are also discussed. We define the first passage time of the ITSS and study its tail behavior. Additionally, we present a time-changed TSS model and highlight its connection to tempered fractional differential equations.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"226 ","pages":"Article 110499"},"PeriodicalIF":0.9,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144604604","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
Upper bounds of spiked covariance matrices under differentially private constrains 微分私有约束下尖刺协方差矩阵的上界
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-06-27 DOI: 10.1016/j.spl.2025.110493
Chunguang Ren, Pei Zhang
{"title":"Upper bounds of spiked covariance matrices under differentially private constrains","authors":"Chunguang Ren,&nbsp;Pei Zhang","doi":"10.1016/j.spl.2025.110493","DOIUrl":"10.1016/j.spl.2025.110493","url":null,"abstract":"<div><div>Cai, Xia, and Zha (2024) presented upper bounds of spiked covariance matrices for Gaussian and sub-Gaussian distributions under the Schatten-q norm, which is a particular type of unitarily invariant norm. In this paper, we also focus on the errors between the true spiked covariance matrices and the covariance matrices with differential privacy under any unitarily invariant norm. Beyond Gaussian and sub-Gaussian populations, we also establish the upper bound of the bounded sub-Gaussian distribution, which is a supplement to the Gaussian and sub-Gaussian cases provided by Cai, Xia, and Zha. It turns out that our estimations are better in some sense.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"226 ","pages":"Article 110493"},"PeriodicalIF":0.9,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144514091","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
Hypothetical versus real life predictions for clusters based finite population total using count and binary survey data 使用计数和二进制调查数据对基于有限人口总数的群集进行假设与现实生活预测
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-06-27 DOI: 10.1016/j.spl.2025.110494
Brajendra C. Sutradhar
{"title":"Hypothetical versus real life predictions for clusters based finite population total using count and binary survey data","authors":"Brajendra C. Sutradhar","doi":"10.1016/j.spl.2025.110494","DOIUrl":"10.1016/j.spl.2025.110494","url":null,"abstract":"<div><div>This paper, as opposed to the existing generalized least square estimation based prediction, provides an optimal estimating function approach with valid prediction for clusters based finite population totals, where within cluster data are supposed to be correlated.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"226 ","pages":"Article 110494"},"PeriodicalIF":0.9,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144518267","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 stochastic competition turbidostat system with general response functions of nutrition: Stationary distribution 具有一般营养响应函数的随机竞争浊化器系统：平稳分布
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-06-24 DOI: 10.1016/j.spl.2025.110492
Xiaojie Mu , Daqing Jiang
{"title":"A stochastic competition turbidostat system with general response functions of nutrition: Stationary distribution","authors":"Xiaojie Mu ,&nbsp;Daqing Jiang","doi":"10.1016/j.spl.2025.110492","DOIUrl":"10.1016/j.spl.2025.110492","url":null,"abstract":"<div><div>We develop and investigate a stochastic competition turbidostat model with environmental noise and general response functions in this contribution. The contents of the turbidostat model are carried out including the existence and uniqueness of global positive equilibrium and stationary distribution. More concretely, the results of this paper are obtained by establishing an appropriate Lyapunov function. In addition, we exhibit a general method for the existence of stationary distribution of competition turbidostat model with environmental noise and general response function by reducing the dimension of the model. Finally, the numerical simulation further verifies theoretical results.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"226 ","pages":"Article 110492"},"PeriodicalIF":0.9,"publicationDate":"2025-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144491337","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
Note on the Anderson–Darling type test for Poisson processes with shift and scale parameters 关于带位移和尺度参数的泊松过程的安德森-达令型试验的说明
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-06-20 DOI: 10.1016/j.spl.2025.110479
A.D. Rafiou , S. Deme , H.G. Izaddine , A.S. Dabye
{"title":"Note on the Anderson–Darling type test for Poisson processes with shift and scale parameters","authors":"A.D. Rafiou ,&nbsp;S. Deme ,&nbsp;H.G. Izaddine ,&nbsp;A.S. Dabye","doi":"10.1016/j.spl.2025.110479","DOIUrl":"10.1016/j.spl.2025.110479","url":null,"abstract":"<div><div>We present a goodness-of-fit test designed for inhomogeneous Poisson processes where the scale and shift parameters are unknown. Our approach involves a test statistic of Anderson–Darling type, and we analyze its asymptotic properties. We prove that, under the null hypothesis, the asymptotic distribution of this statistic is independent of the unknown parameters. Additionally, we establish that the Anderson–Darling type test is consistent for the alternative hypothesis.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"226 ","pages":"Article 110479"},"PeriodicalIF":0.9,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144524254","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 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
Sampling random spanning arborescences in graphs with low conductance 低电导图中随机生成树形的抽样
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-06-16 DOI: 10.1016/j.spl.2025.110481
Vittorio Zampinetti , Harald Melin , Jens Lagergren
{"title":"Sampling random spanning arborescences in graphs with low conductance","authors":"Vittorio Zampinetti ,&nbsp;Harald Melin ,&nbsp;Jens Lagergren","doi":"10.1016/j.spl.2025.110481","DOIUrl":"10.1016/j.spl.2025.110481","url":null,"abstract":"<div><div>Sampling random spanning arborescences in directed graphs is critical for applications in network analysis, optimization, and machine learning. While many state-of-the-art methods perform well on graphs with high conductance, they often fail or generalize poorly on low-conductance graphs. Inspired by Wilson’s algorithm, we propose a novel sampling approach that overcomes this limitation by using dynamic programming to compute random walk probabilities. This avoids both inefficient walk simulations and numerically unstable Laplacian determinant calculations. Our method demonstrates superior efficiency and sampling quality in simulations, and is the only one to handle low-conductance graphs effectively.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"226 ","pages":"Article 110481"},"PeriodicalIF":0.9,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144481049","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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