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A note on the maximum probability of ultra log-concave distributions 关于超对数凹分布的最大概率的注释
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-04-10 DOI: 10.1016/j.spl.2025.110418
Heshan Aravinda
{"title":"A note on the maximum probability of ultra log-concave distributions","authors":"Heshan Aravinda","doi":"10.1016/j.spl.2025.110418","DOIUrl":"10.1016/j.spl.2025.110418","url":null,"abstract":"<div><div>Jakimiuk et al. (2024) have proved that, if <span><math><mi>X</mi></math></span> is an ultra log-concave random variable with integral mean, then <span><math><mrow><munder><mrow><mo>max</mo></mrow><mrow><mi>n</mi></mrow></munder><mi>P</mi><mrow><mo>{</mo><mi>X</mi><mo>=</mo><mi>n</mi><mo>}</mo></mrow><mo>≥</mo><munder><mrow><mo>max</mo></mrow><mrow><mi>n</mi></mrow></munder><mi>P</mi><mrow><mo>{</mo><mi>Z</mi><mo>=</mo><mi>n</mi><mo>}</mo></mrow><mo>,</mo><mspace></mspace></mrow></math></span> where <span><math><mi>Z</mi></math></span> is a Poisson random variable with the parameter <span><math><mrow><mi>E</mi><mrow><mo>[</mo><mi>X</mi><mo>]</mo></mrow></mrow></math></span>. In this note, we show that this inequality does not always hold true when <span><math><mi>X</mi></math></span> is ultra log-concave with <span><math><mrow><mi>E</mi><mrow><mo>[</mo><mi>X</mi><mo>]</mo></mrow><mo>&gt;</mo><mn>1</mn></mrow></math></span>.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"223 ","pages":"Article 110418"},"PeriodicalIF":0.9,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143823885","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 reflected backward stochastic differential equations with jumps in a convex domain 均值反映了凸域中具有跳跃的后向随机微分方程
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-04-10 DOI: 10.1016/j.spl.2025.110426
Hongchao Qian
{"title":"Mean reflected backward stochastic differential equations with jumps in a convex domain","authors":"Hongchao Qian","doi":"10.1016/j.spl.2025.110426","DOIUrl":"10.1016/j.spl.2025.110426","url":null,"abstract":"<div><div>In this paper, we study a class of multi-dimensional mean reflected backward stochastic differential equations driven by a Brownian motion and an independent Poisson random measure. In our setting, the constraint depends on the law of the solution rather than on its paths. Specifically, the expectation of the solution takes values in a convex domain in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. The existence and uniqueness of solutions are established by a penalization method.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"223 ","pages":"Article 110426"},"PeriodicalIF":0.9,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143815702","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
Lp-solutions of backward stochastic differential equations with default time 具有默认时间的倒向随机微分方程的lp解
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-04-09 DOI: 10.1016/j.spl.2025.110407
Badr Elmansouri , Mohamed Marzougue
{"title":"Lp-solutions of backward stochastic differential equations with default time","authors":"Badr Elmansouri ,&nbsp;Mohamed Marzougue","doi":"10.1016/j.spl.2025.110407","DOIUrl":"10.1016/j.spl.2025.110407","url":null,"abstract":"<div><div>In this paper, we address the problem of existence and uniqueness of <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-solutions for backward stochastic differential equations (BSDEs) with default time, for <span><math><mrow><mi>p</mi><mo>∈</mo><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span>. Under appropriate <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-integrability conditions on the data and a <span><math><mi>γ</mi></math></span>-Lipschitz condition on the coefficient, where <span><math><mi>γ</mi></math></span> is the intensity process of the martingale associated with the default jump, we prove the existence and uniqueness of an <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-solution.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"223 ","pages":"Article 110407"},"PeriodicalIF":0.9,"publicationDate":"2025-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143815701","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
Lower bounds for density estimation on symmetric spaces 对称空间上密度估计的下界
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-03-31 DOI: 10.1016/j.spl.2025.110416
Dena Marie Asta
{"title":"Lower bounds for density estimation on symmetric spaces","authors":"Dena Marie Asta","doi":"10.1016/j.spl.2025.110416","DOIUrl":"10.1016/j.spl.2025.110416","url":null,"abstract":"<div><div>We prove that kernel density estimation on symmetric spaces of non-compact type, whose <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-risk was bounded above in previous work (Asta, 2021), in fact achieves a minimax rate of convergence. With this result, the story for kernel density estimation on all symmetric spaces is completed. The idea in adapting the proof for Euclidean space is to suitably abstract vector space operations on Euclidean space to both actions of symmetric groups and reparametrizations of Helgason–Fourier transforms and to use the fact that the exponential map for symmetric spaces of non-compact type defines a diffeomorphism.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"223 ","pages":"Article 110416"},"PeriodicalIF":0.9,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759730","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
Posterior model consistency in high-dimensional Bayesian variable selection with arbitrary priors 任意先验条件下高维贝叶斯变量选择的后验模型一致性
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-03-28 DOI: 10.1016/j.spl.2025.110415
Min Hua , Gyuhyeong Goh
{"title":"Posterior model consistency in high-dimensional Bayesian variable selection with arbitrary priors","authors":"Min Hua ,&nbsp;Gyuhyeong Goh","doi":"10.1016/j.spl.2025.110415","DOIUrl":"10.1016/j.spl.2025.110415","url":null,"abstract":"<div><div>In the context of Bayesian regression modeling, posterior model consistency provides frequentist validation for Bayesian variable selection. A question that has long been open is whether posterior model consistency holds under arbitrary priors when high-dimensional variable selection is performed. In this paper, we aim to give an answer by establishing sufficient conditions for priors under which the posterior model distribution converges to a degenerate distribution at the true model. Our framework considers high-dimensional regression settings where the number of potential predictors grows at a rate faster than the sample size. We demonstrate that a wide selection of priors satisfy the conditions that we establish in this paper.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"223 ","pages":"Article 110415"},"PeriodicalIF":0.9,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143734875","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 impact of contamination and correlated design on the Lasso: An average case analysis 污染和相关设计对套索的影响：一个平均案例分析
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-03-28 DOI: 10.1016/j.spl.2025.110417
Stanislav Minsker , Yiqiu Shen
{"title":"The impact of contamination and correlated design on the Lasso: An average case analysis","authors":"Stanislav Minsker ,&nbsp;Yiqiu Shen","doi":"10.1016/j.spl.2025.110417","DOIUrl":"10.1016/j.spl.2025.110417","url":null,"abstract":"<div><div>We study the prediction problem in the context of the high-dimensional linear regression model. We focus on the practically relevant framework where a fraction of the linear measurements is corrupted while the columns of the design matrix can be moderately correlated. Our findings suggest that for most sparse signals, the Lasso estimator admits strong performance guarantees under more easily verifiable and less stringent assumptions on the design matrix compared to much of the existing literature.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"223 ","pages":"Article 110417"},"PeriodicalIF":0.9,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759731","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
Solution to a generalized FBSDE with delay and anticipated terms and applications to control problem with time-varying delay 一类具有时滞和预期项的广义FBSDE的求解及其在时变时滞控制问题中的应用
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-03-25 DOI: 10.1016/j.spl.2025.110414
Yuecai Han , Yuhang Li , Zheng Li
{"title":"Solution to a generalized FBSDE with delay and anticipated terms and applications to control problem with time-varying delay","authors":"Yuecai Han ,&nbsp;Yuhang Li ,&nbsp;Zheng Li","doi":"10.1016/j.spl.2025.110414","DOIUrl":"10.1016/j.spl.2025.110414","url":null,"abstract":"<div><div>In this paper, motivated by optimal control problem with time-varying delay, we study a type of generalized forward–backward stochastic differential equation. Both delay and anticipated terms appear in both forward equation and backward equation. The existence and uniqueness of the solution is obtained. As an application, the linear quadratic optimal control problem, where both state process and control process contain time-varying delay, is solved.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"223 ","pages":"Article 110414"},"PeriodicalIF":0.9,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143705736","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 novel approach for estimating multi-attribute Gaussian copula graphical models 一种估计多属性高斯联结图模型的新方法
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-03-24 DOI: 10.1016/j.spl.2025.110413
Lijie Li , Yang Yu , Wanfeng Liang , Feng Zou
{"title":"A novel approach for estimating multi-attribute Gaussian copula graphical models","authors":"Lijie Li ,&nbsp;Yang Yu ,&nbsp;Wanfeng Liang ,&nbsp;Feng Zou","doi":"10.1016/j.spl.2025.110413","DOIUrl":"10.1016/j.spl.2025.110413","url":null,"abstract":"<div><div>This paper considers estimating multi-attribute Gaussian copula graphical models where each node represents multivariate variables with rich meanings. A two-stage semiparametric method is proposed to achieve modeling flexibility and estimation robustness simultaneously by utilizing normal score transformation. We derive the consistency of the proposed estimator under the spectral norm, and establish the theoretical guarantees on sparsistency under some mild conditions. Simulation studies and a real data example are provided to demonstrate the empirical performance of the proposed method. We provide the complete code supporting this article at <span><span>https://github.com/JerryLi-Stat/Multi-attribute-GCGM</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"222 ","pages":"Article 110413"},"PeriodicalIF":0.9,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683346","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
Transportation cost inequalities for the stochastic Ginzburg–Landau equation driven by space–time white noises 时空白噪声驱动下随机金兹堡-朗道方程的运输成本不等式
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-03-24 DOI: 10.1016/j.spl.2025.110409
Beibei Zhang
{"title":"Transportation cost inequalities for the stochastic Ginzburg–Landau equation driven by space–time white noises","authors":"Beibei Zhang","doi":"10.1016/j.spl.2025.110409","DOIUrl":"10.1016/j.spl.2025.110409","url":null,"abstract":"<div><div>In this paper, we establish transportation cost inequalities for the solution of the stochastic complex Ginzburg–Landau equation driven by a space–time white noise on the spaces <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo></mrow><mo>×</mo><mi>D</mi><mo>)</mo></mrow></mrow></math></span> or <span><math><mrow><mi>C</mi><mrow><mo>(</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo></mrow><mo>;</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>D</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow></math></span>. The proof is based on the estimates of the nonlinear term.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"222 ","pages":"Article 110409"},"PeriodicalIF":0.9,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143696877","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 local long-time behaviour for continuous-time branching processes 连续时间分支过程的局部长时间行为
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-03-24 DOI: 10.1016/j.spl.2025.110412
Liuyan Li , Junping Li
{"title":"The local long-time behaviour for continuous-time branching processes","authors":"Liuyan Li ,&nbsp;Junping Li","doi":"10.1016/j.spl.2025.110412","DOIUrl":"10.1016/j.spl.2025.110412","url":null,"abstract":"<div><div>Let <span><math><mrow><mo>{</mo><mi>Z</mi><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 continuous-time branching process. There is a normalizing function <span><math><msub><mrow><mi>γ</mi></mrow><mrow><mi>t</mi></mrow></msub></math></span> such that <span><math><mrow><mi>Z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><msub><mrow><mi>γ</mi></mrow><mrow><mi>t</mi></mrow></msub></mrow></math></span> converges almost surely to a random variable. In this paper, we obtain a local limit theorem for <span><math><mrow><mo>{</mo><mi>Z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>;</mo><mi>t</mi><mo>≥</mo><mn>0</mn><mo>}</mo></mrow></math></span>, which refers to the asymptotic behaviour of <span><math><mrow><mi>P</mi><mrow><mo>(</mo><mi>Z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><msub><mrow><mi>k</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>)</mo></mrow></mrow></math></span> with <span><math><mrow><munder><mrow><mo>lim</mo></mrow><mrow><mi>t</mi><mo>→</mo><mi>∞</mi></mrow></munder><msub><mrow><mi>k</mi></mrow><mrow><mi>t</mi></mrow></msub><msub><mrow><mi>γ</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>x</mi></mrow></math></span> and <span><math><mrow><mi>x</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>. This expands the existing results of the discrete-time branching processes.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"223 ","pages":"Article 110412"},"PeriodicalIF":0.9,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143715864","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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