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Minimax optimality of kernel ridge regression when kernel eigenvalues decay polynomially or exponentially 核特征值多项式或指数衰减时核脊回归的极大极小最优性
IF 0.7 4区 数学
Statistics & Probability Letters Pub Date : 2025-08-21 DOI: 10.1016/j.spl.2025.110526
Kwan-Young Bak , Woojoo Lee
{"title":"Minimax optimality of kernel ridge regression when kernel eigenvalues decay polynomially or exponentially","authors":"Kwan-Young Bak ,&nbsp;Woojoo Lee","doi":"10.1016/j.spl.2025.110526","DOIUrl":"10.1016/j.spl.2025.110526","url":null,"abstract":"<div><div>We investigate the minimax optimality of the kernel ridge regression by quantifying the estimation complexity owing to the dimensionality under the polynomial or exponential decay rates of the kernel function’s eigenvalues. Based on this result, we elucidate why certain <span><math><mi>d</mi></math></span>-dimensional spaces allow us to bypass the curse of dimensionality in nonparametric function estimation, because the convergence rates are bounded by those of the univariate case, with a logarithmic factor raised to a power determined by the dimension. Our results reveal that convergence rates with logarithmic factors are generally uniformly unimprovable.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110526"},"PeriodicalIF":0.7,"publicationDate":"2025-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144891864","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-optimal design for Becker’s minimum polynomial with upper and lower bound constraints 具有上界和下界约束的Becker最小多项式的最优设计
IF 0.7 4区 数学
Statistics & Probability Letters Pub Date : 2025-08-20 DOI: 10.1016/j.spl.2025.110534
Junpeng Li , Guanghui Li , Chongqi Zhang
{"title":"A-optimal design for Becker’s minimum polynomial with upper and lower bound constraints","authors":"Junpeng Li ,&nbsp;Guanghui Li ,&nbsp;Chongqi Zhang","doi":"10.1016/j.spl.2025.110534","DOIUrl":"10.1016/j.spl.2025.110534","url":null,"abstract":"<div><div>This paper investigates the <span><math><mi>A</mi></math></span>-optimal design of Becker’s minimum polynomial of order 2 with upper and lower bound constraints. It also provides the necessary results to obtain the <span><math><mi>A</mi></math></span>-optimal designs on <span><math><mi>L</mi></math></span>-simplex and <span><math><mi>U</mi></math></span>-simplex.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110534"},"PeriodicalIF":0.7,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144892979","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 note on the geodesic normal distribution on the sphere 球面上测地线正态分布的注释
IF 0.7 4区 数学
Statistics & Probability Letters Pub Date : 2025-08-19 DOI: 10.1016/j.spl.2025.110532
José E. Chacón , Andrea Meilán-Vila
{"title":"A note on the geodesic normal distribution on the sphere","authors":"José E. Chacón ,&nbsp;Andrea Meilán-Vila","doi":"10.1016/j.spl.2025.110532","DOIUrl":"10.1016/j.spl.2025.110532","url":null,"abstract":"<div><div>This paper presents an alternative formulation of the geodesic normal distribution on the sphere, building on the work of <span><span>Hauberg (2018)</span></span>. While the isotropic version of this distribution is naturally defined on the sphere, the anisotropic version requires projecting points from the sphere onto the tangent space. In contrast, our approach removes the dependence on the tangent space and defines the geodesic normal distribution directly on the sphere. Moreover, we demonstrate that the density contours of this distribution are exactly ellipses on the sphere, providing intriguing alternative characterizations for describing this locus of points.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110532"},"PeriodicalIF":0.7,"publicationDate":"2025-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144908721","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
Limit theorems for renewal processes with infinite mean interarrival time under random inspection 随机检查下具有无限平均到达间隔时间的更新过程的极限定理
IF 0.7 4区 数学
Statistics & Probability Letters Pub Date : 2025-08-18 DOI: 10.1016/j.spl.2025.110527
Diana Rauwolf
{"title":"Limit theorems for renewal processes with infinite mean interarrival time under random inspection","authors":"Diana Rauwolf","doi":"10.1016/j.spl.2025.110527","DOIUrl":"10.1016/j.spl.2025.110527","url":null,"abstract":"<div><div>Analogues to fundamental asymptotic relations in renewal theory are considered under the assumption that the time is a random variable and that the interarrival times have infinite mean. Limits are given for interarrival times with regularly varying tail and for sequences of parameters of the respective random-time distribution under mild conditions. An application to alternating renewal processes is shown.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110527"},"PeriodicalIF":0.7,"publicationDate":"2025-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144878116","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
Asymptotic behavior of finite-time ruin probabilities in a bidimensional compound risk model 二维复合风险模型有限时间破产概率的渐近行为
IF 0.7 4区 数学
Statistics & Probability Letters Pub Date : 2025-08-18 DOI: 10.1016/j.spl.2025.110529
Jinjin Zhang , Yang Yang , Lin Xu
{"title":"Asymptotic behavior of finite-time ruin probabilities in a bidimensional compound risk model","authors":"Jinjin Zhang ,&nbsp;Yang Yang ,&nbsp;Lin Xu","doi":"10.1016/j.spl.2025.110529","DOIUrl":"10.1016/j.spl.2025.110529","url":null,"abstract":"<div><div>Consider a bidimensional compound risk model with stochastic premiums and returns, in which an insurer makes both risk-free and risky investments in two lines of business, and an accident may cause more than one claim. In this model, we allow that the two log-price processes are both real-valued Lévy processes, the claim numbers from the same business line, the two accident arrival processes and the two premium processes from two business lines are, respectively, arbitrarily dependent, and the premium processes are also arbitrarily dependent on all other random sources except the log-price processes. Under the condition that all claims from the same line are pairwise quasi-asymptotically independent and consistently varying-tailed, this paper establishes the asymptotic formulas for two types of finite-time ruin probabilities.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110529"},"PeriodicalIF":0.7,"publicationDate":"2025-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144864936","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
Fractional signature: A generalisation of the signature inspired by fractional calculus 分数签名：由分数微积分启发的签名的推广
IF 0.7 4区 数学
Statistics & Probability Letters Pub Date : 2025-08-18 DOI: 10.1016/j.spl.2025.110533
José Manuel Corcuera, Rubén Jiménez
{"title":"Fractional signature: A generalisation of the signature inspired by fractional calculus","authors":"José Manuel Corcuera,&nbsp;Rubén Jiménez","doi":"10.1016/j.spl.2025.110533","DOIUrl":"10.1016/j.spl.2025.110533","url":null,"abstract":"<div><div>In this paper, we propose a novel generalisation of the signature of a path, motivated by fractional calculus, which is able to describe the solutions of linear Caputo controlled FDEs. We also propose another generalisation of the signature, inspired by the previous one, but more convenient to use in machine learning. Finally, we test this last signature in a toy application to the problem of handwritten digit recognition, where significant improvements in accuracy rates are observed compared to those of the original signature.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110533"},"PeriodicalIF":0.7,"publicationDate":"2025-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144864938","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
Space–time fractional diffusion with stochastic resetting 随机重置的时空分数扩散
IF 0.7 4区 数学
Statistics & Probability Letters Pub Date : 2025-08-18 DOI: 10.1016/j.spl.2025.110528
Priti, Arun Kumar
{"title":"Space–time fractional diffusion with stochastic resetting","authors":"Priti,&nbsp;Arun Kumar","doi":"10.1016/j.spl.2025.110528","DOIUrl":"10.1016/j.spl.2025.110528","url":null,"abstract":"<div><div>In this article, we study the space–time fractional diffusion equation (STFDE) which is a generalization of the classical diffusion equation, in the presence of stochastic resetting. The STFDE is formulated by replacing the standard time and space derivatives with the Caputo and Riesz fractional derivatives, respectively, to capture anomalous diffusion behaviors. We derive analytical solutions using Laplace and Fourier transforms, and express them in terms of Fox H-functions. We obtain a closed-form expression for the stationary distribution and prove the finiteness of the mean first passage time. Additionally, we examine how stochastic resetting influences the infinite divisibility of the standard diffusion process, showing that this property is lost once resetting is introduced. The reset mechanism interrupts the Lévy process at random times, effectively altering the jump structure and destroying the self-decomposability required for infinite divisibility.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110528"},"PeriodicalIF":0.7,"publicationDate":"2025-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144864935","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
Random bridges in spaces of growing dimension 在不断增长的维度空间中的随机桥
IF 0.7 4区 数学
Statistics & Probability Letters Pub Date : 2025-08-16 DOI: 10.1016/j.spl.2025.110530
Bochen Jin
{"title":"Random bridges in spaces of growing dimension","authors":"Bochen Jin","doi":"10.1016/j.spl.2025.110530","DOIUrl":"10.1016/j.spl.2025.110530","url":null,"abstract":"<div><div>We investigate the limiting behaviour of the path of random bridges treated as random sets in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> with the Euclidean metric and the dimension <span><math><mi>d</mi></math></span> increasing to infinity. The main result states that, in the square integrable case, the limit (in the Gromov–Hausdorff sense) is deterministic, namely, it is <span><math><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></math></span> equipped with the pseudo-metric <span><math><msqrt><mrow><mrow><mo>|</mo><mi>t</mi><mo>−</mo><mi>s</mi><mo>|</mo></mrow><mrow><mo>(</mo><mn>1</mn><mo>−</mo><mrow><mo>|</mo><mi>t</mi><mo>−</mo><mi>s</mi><mo>|</mo></mrow><mo>)</mo></mrow></mrow></msqrt></math></span>. We also show that, in the heavy-tailed case with summands regularly varying of order <span><math><mrow><mi>α</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>, the limiting metric space has a random metric derived from the bridge variant of a subordinator.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110530"},"PeriodicalIF":0.7,"publicationDate":"2025-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144864937","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 note on three new bounds of Tsallis entropy 关于萨利斯熵的三个新边界的注解
IF 0.7 4区 数学
Statistics & Probability Letters Pub Date : 2025-08-14 DOI: 10.1016/j.spl.2025.110524
Panxu Yuan , Zhenfeng Zou
{"title":"A note on three new bounds of Tsallis entropy","authors":"Panxu Yuan ,&nbsp;Zhenfeng Zou","doi":"10.1016/j.spl.2025.110524","DOIUrl":"10.1016/j.spl.2025.110524","url":null,"abstract":"<div><div>Tsallis entropy is a commonly used uncertainty measure in information theory. In this paper, three new bounds of Tsallis entropy are provided for discrete random variables with finite support. This improves the understanding of the information content in complex systems.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110524"},"PeriodicalIF":0.7,"publicationDate":"2025-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144860661","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 Borel–Cantelli lemma under m-dependence m依赖下的Borel-Cantelli引理
IF 0.7 4区 数学
Statistics & Probability Letters Pub Date : 2025-08-13 DOI: 10.1016/j.spl.2025.110525
Dawei Lu, Yunpeng Shi, Junhan Zhao
{"title":"The Borel–Cantelli lemma under m-dependence","authors":"Dawei Lu,&nbsp;Yunpeng Shi,&nbsp;Junhan Zhao","doi":"10.1016/j.spl.2025.110525","DOIUrl":"10.1016/j.spl.2025.110525","url":null,"abstract":"<div><div>Let <span><math><msubsup><mrow><mrow><mo>{</mo><msub><mrow><mi>A</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>}</mo></mrow></mrow><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>∞</mi></mrow></msubsup></math></span> be an <span><math><mi>m</mi></math></span>-dependent sequence of events. In this paper, we proved the second part of the Borel–Cantelli lemma still holds under <span><math><mi>m</mi></math></span>-dependence. Furthermore, we also obtained the quantitative version of this result.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110525"},"PeriodicalIF":0.7,"publicationDate":"2025-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144860297","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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