Pub Date : 2025-09-03DOI: 10.1016/j.spl.2025.110546
Zhenlong Gao
Consider a supercritical continuous time branching process called randomly indexed branching processes with immigration. Large deviation results are established for the logarithms of such processes. Our results show that when the offspring distribution belongs to the Schröder case, the immigration distribution affects the rate function of the large deviation, while when the offspring distribution belongs to the Böttcher case, the immigration distribution has no effect on the rate function.
{"title":"Large deviations for a randomly indexed branching process with immigration","authors":"Zhenlong Gao","doi":"10.1016/j.spl.2025.110546","DOIUrl":"10.1016/j.spl.2025.110546","url":null,"abstract":"<div><div>Consider a supercritical continuous time branching process called randomly indexed branching processes with immigration. Large deviation results are established for the logarithms of such processes. Our results show that when the offspring distribution belongs to the Schröder case, the immigration distribution affects the rate function of the large deviation, while when the offspring distribution belongs to the Böttcher case, the immigration distribution has no effect on the rate function.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110546"},"PeriodicalIF":0.7,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145010249","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}
Pub Date : 2025-09-03DOI: 10.1016/j.spl.2025.110552
Haruhiko Ogasawara
Gaussian product inequalities (GPIs) for absolute raw moments of real-valued orders are shown, where the orders include negative signs and mixed ones (positive and negative). The GPIs are for structural correlation matrices with a single parameter showing compound symmetric and autoregressive patterns with a non-zero common mean in each model. In the bivariate case, we have an extended so-called opposite GPI for the absolute raw moments. The GPIs are obtained by a known series formula of the Gaussian product absolute raw moments.
{"title":"Gaussian product inequalities for absolute raw moments","authors":"Haruhiko Ogasawara","doi":"10.1016/j.spl.2025.110552","DOIUrl":"10.1016/j.spl.2025.110552","url":null,"abstract":"<div><div>Gaussian product inequalities (GPIs) for absolute raw moments of real-valued orders are shown, where the orders include negative signs and mixed ones (positive and negative). The GPIs are for structural correlation matrices with a single parameter showing compound symmetric and autoregressive patterns with a non-zero common mean in each model. In the bivariate case, we have an extended so-called opposite GPI for the absolute raw moments. The GPIs are obtained by a known series formula of the Gaussian product absolute raw moments.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110552"},"PeriodicalIF":0.7,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145019574","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}
Pub Date : 2025-09-03DOI: 10.1016/j.spl.2025.110547
Heguang Liu
In this paper, under certain conditions, we investigate the asymptotic behavior of , where is the density of symmetric -stable random variables with and is some self-similar Gaussian process with index . We mainly focus on the critical case and the subcritical case . This work will extend the corresponding results in Hong et al. (2024) and may give another definition for the fractional derivative of local times of the Gaussian process .
在一定条件下，研究了{∫0tfα(nH(Xs−λ))ds，t≥0}的渐近性，其中，fα是α∈(0,2)且X={Xt，t≥0}的对称α-稳定随机变量的密度，是索引H∈(0,1)的自相似高斯过程。我们主要关注临界情况H(2α+1)=1和亚临界情况H(2α+1)<1。这项工作将扩展Hong et al.（2024）的相应结果，并可能给出高斯过程X局部时间的分数阶导数的另一种定义。
{"title":"Functional limit theorems for some self-similar Gaussian processes in critical and subcritical cases","authors":"Heguang Liu","doi":"10.1016/j.spl.2025.110547","DOIUrl":"10.1016/j.spl.2025.110547","url":null,"abstract":"<div><div>In this paper, under certain conditions, we investigate the asymptotic behavior of <span><math><mrow><mo>{</mo><msubsup><mrow><mo>∫</mo></mrow><mrow><mn>0</mn></mrow><mrow><mi>t</mi></mrow></msubsup><msub><mrow><mi>f</mi></mrow><mrow><mi>α</mi></mrow></msub><mrow><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mi>H</mi></mrow></msup><mrow><mo>(</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>−</mo><mi>λ</mi><mo>)</mo></mrow><mo>)</mo></mrow><mspace></mspace><mi>d</mi><mi>s</mi><mo>,</mo><mspace></mspace><mi>t</mi><mo>≥</mo><mn>0</mn><mo>}</mo></mrow></math></span>, where <span><math><msub><mrow><mi>f</mi></mrow><mrow><mi>α</mi></mrow></msub></math></span> is the density of symmetric <span><math><mi>α</mi></math></span>-stable random variables with <span><math><mrow><mi>α</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>X</mi><mo>=</mo><mrow><mo>{</mo><mrow><msub><mrow><mi>X</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>,</mo><mspace></mspace><mi>t</mi><mo>≥</mo><mn>0</mn></mrow><mo>}</mo></mrow></mrow></math></span> is some self-similar Gaussian process with index <span><math><mrow><mi>H</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>. We mainly focus on the critical case <span><math><mrow><mi>H</mi><mrow><mo>(</mo><mn>2</mn><mi>α</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mo>=</mo><mn>1</mn></mrow></math></span> and the subcritical case <span><math><mrow><mi>H</mi><mrow><mo>(</mo><mn>2</mn><mi>α</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mo><</mo><mn>1</mn></mrow></math></span>. This work will extend the corresponding results in Hong et al. (2024) and may give another definition for the fractional derivative of local times of the Gaussian process <span><math><mi>X</mi></math></span>.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110547"},"PeriodicalIF":0.7,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145026630","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}
Pub Date : 2025-08-28DOI: 10.1016/j.spl.2025.110531
Matthias Kirchner
This brief paper identifies the Palm distribution of a linear Hawkes process. The textbook example for Palm distributions is the Palm version of a stationary Poisson process that corresponds to the original process plus a point in zero. The present result generalizes this example in a more complex but nevertheless tractable way. As a next step, we derive the intensity measure of the Palm version of a Hawkes process and show how it could be used for estimation. Finally, we discuss further possible applications to the theory of Hawkes processes.
{"title":"Palm versions of Hawkes processes","authors":"Matthias Kirchner","doi":"10.1016/j.spl.2025.110531","DOIUrl":"10.1016/j.spl.2025.110531","url":null,"abstract":"<div><div>This brief paper identifies the Palm distribution of a linear Hawkes process. The textbook example for Palm distributions is the Palm version of a stationary Poisson process that corresponds to the original process plus a point in zero. The present result generalizes this example in a more complex but nevertheless tractable way. As a next step, we derive the intensity measure of the Palm version of a Hawkes process and show how it could be used for estimation. Finally, we discuss further possible applications to the theory of Hawkes processes.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110531"},"PeriodicalIF":0.7,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144917648","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}
Pub Date : 2025-08-23DOI: 10.1016/j.spl.2025.110535
Koki Shimizu, Hiroki Hashiguchi
This paper discusses the distribution of the eigenvalues of a gamma matrix, which is generated from the product of an extended Gaussian matrix and its transposed matrix. We show that the distributions of the individual eigenvalues of a gamma matrix are approximated by the univariate gamma distribution when the first few eigenvalues of the scale parameter matrix are infinitely dispersed. Our results cover the eigenvalue distributions under the Gaussian and Kotz-type I models as special cases.
{"title":"Approximate distribution of eigenvalues of a generalized Wishart matrix under an extended Gaussian model","authors":"Koki Shimizu, Hiroki Hashiguchi","doi":"10.1016/j.spl.2025.110535","DOIUrl":"10.1016/j.spl.2025.110535","url":null,"abstract":"<div><div>This paper discusses the distribution of the eigenvalues of a gamma matrix, which is generated from the product of an extended Gaussian matrix and its transposed matrix. We show that the distributions of the individual eigenvalues of a gamma matrix are approximated by the univariate gamma distribution when the first few eigenvalues of the scale parameter matrix are infinitely dispersed. Our results cover the eigenvalue distributions under the Gaussian and Kotz-type I models as special cases.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110535"},"PeriodicalIF":0.7,"publicationDate":"2025-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144921177","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}
Pub Date : 2025-08-22DOI: 10.1016/j.spl.2025.110536
Yves Tillé
This paper introduces a straightforward method for selecting a balanced random sample from a population. The procedure involves a flight phase, which transforms the vector of inclusion probabilities into one with components close to 0 or 1, followed by a landing phase to complete the selection. We present a novel implementation of the flight phase that leverages linear programming, enabling a highly concise and easily interpretable R code. The method is formally described, implemented in R, and illustrated using real population data. This approach offers a practical, transparent, and reproducible solution to the balanced sampling problem, while establishing a direct link to linear programming techniques.
{"title":"A practical flight-phase approach to balanced random sampling","authors":"Yves Tillé","doi":"10.1016/j.spl.2025.110536","DOIUrl":"10.1016/j.spl.2025.110536","url":null,"abstract":"<div><div>This paper introduces a straightforward method for selecting a balanced random sample from a population. The procedure involves a flight phase, which transforms the vector of inclusion probabilities into one with components close to 0 or 1, followed by a landing phase to complete the selection. We present a novel implementation of the flight phase that leverages linear programming, enabling a highly concise and easily interpretable R code. The method is formally described, implemented in R, and illustrated using real population data. This approach offers a practical, transparent, and reproducible solution to the balanced sampling problem, while establishing a direct link to linear programming techniques.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110536"},"PeriodicalIF":0.7,"publicationDate":"2025-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144892980","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}
Pub Date : 2025-08-21DOI: 10.1016/j.spl.2025.110526
Kwan-Young Bak , Woojoo Lee
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 -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.
{"title":"Minimax optimality of kernel ridge regression when kernel eigenvalues decay polynomially or exponentially","authors":"Kwan-Young Bak , 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}
Pub Date : 2025-08-20DOI: 10.1016/j.spl.2025.110534
Junpeng Li , Guanghui Li , Chongqi Zhang
This paper investigates the -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 -optimal designs on -simplex and -simplex.
{"title":"A-optimal design for Becker’s minimum polynomial with upper and lower bound constraints","authors":"Junpeng Li , Guanghui Li , 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}
Pub Date : 2025-08-19DOI: 10.1016/j.spl.2025.110532
José E. Chacón , Andrea Meilán-Vila
This paper presents an alternative formulation of the geodesic normal distribution on the sphere, building on the work of Hauberg (2018). 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.
{"title":"A note on the geodesic normal distribution on the sphere","authors":"José E. Chacón , 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}
Pub Date : 2025-08-18DOI: 10.1016/j.spl.2025.110527
Diana Rauwolf
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.
{"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}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号