Statistics & Probability Letters最新文献

{"title":"Iterated ergodic theorems and Erdös–Rényi law of large numbers","authors":"Yuri Kifer","doi":"10.1016/j.spl.2025.110572","DOIUrl":"10.1016/j.spl.2025.110572","url":null,"abstract":"<div><div>We obtain ergodic theorems and a version of the Erdös–Rènyi law of large numbers for multiple iterated sums and integrals of the form <span><math><mrow><msup><mrow><mi>Σ</mi></mrow><mrow><mrow><mo>(</mo><mi>ν</mi><mo>)</mo></mrow></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><msub><mrow><mo>∑</mo></mrow><mrow><mn>0</mn><mo>≤</mo><msub><mrow><mi>k</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>&lt;</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>&lt;</mo><msub><mrow><mi>k</mi></mrow><mrow><mi>ν</mi></mrow></msub><mo>≤</mo><mi>t</mi></mrow></msub><mi>ξ</mi><mrow><mo>(</mo><msub><mrow><mi>k</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo></mrow><mo>⊗</mo><mo>⋯</mo><mo>⊗</mo><mi>ξ</mi><mrow><mo>(</mo><msub><mrow><mi>k</mi></mrow><mrow><mi>ν</mi></mrow></msub><mo>)</mo></mrow></mrow></math></span>, <span><math><mrow><mi>t</mi><mo>∈</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo></mrow></mrow></math></span> and <span><math><mrow><msup><mrow><mi>Σ</mi></mrow><mrow><mrow><mo>(</mo><mi>ν</mi><mo>)</mo></mrow></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><msub><mrow><mo>∫</mo></mrow><mrow><mn>0</mn><mo>≤</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>≤</mo><mo>⋯</mo><mo>≤</mo><msub><mrow><mi>s</mi></mrow><mrow><mi>ν</mi></mrow></msub><mo>≤</mo><mi>t</mi></mrow></msub><mi>ξ</mi><mrow><mo>(</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo></mrow><mo>⊗</mo><mo>⋯</mo><mo>⊗</mo><mi>ξ</mi><mrow><mo>(</mo><msub><mrow><mi>s</mi></mrow><mrow><mi>ν</mi></mrow></msub><mo>)</mo></mrow><mi>d</mi><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>⋯</mo><mi>d</mi><msub><mrow><mi>s</mi></mrow><mrow><mi>ν</mi></mrow></msub></mrow></math></span> where <span><math><msub><mrow><mrow><mo>{</mo><mi>ξ</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mo>}</mo></mrow></mrow><mrow><mo>−</mo><mi>∞</mi><mo>&lt;</mo><mi>k</mi><mo>&lt;</mo><mi>∞</mi></mrow></msub></math></span> and <span><math><msub><mrow><mrow><mo>{</mo><mi>ξ</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow><mo>}</mo></mrow></mrow><mrow><mo>−</mo><mi>∞</mi><mo>&lt;</mo><mi>s</mi><mo>&lt;</mo><mi>∞</mi></mrow></msub></math></span> are stationary vector stochastic processes.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"228 ","pages":"Article 110572"},"PeriodicalIF":0.7,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222580","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}

{"title":"Change-point detection in Vector-Tensor linear model","authors":"Haiyue Su ,&nbsp;Zhiming Xia ,&nbsp;Wenyuan Shang ,&nbsp;Meili Shi","doi":"10.1016/j.spl.2025.110563","DOIUrl":"10.1016/j.spl.2025.110563","url":null,"abstract":"<div><div>For high-throughput low-rank data, CANDECOMP/PARAFAC (<span><math><mi>CP</mi></math></span>) decomposition is frequently employed to reduce the dimensionality to a manageable level. In this article, we consider a Vector-Tensor linear regression model, where the low-rank structure is expressed through CP decomposition, and the change-point structure is incorporated into the multi-array coefficients. A novel procedure is proposed to jointly detect the change-point and estimate the tensor structure by minimizing the sum of squared residuals. The associated algorithm is developed based on Alternating Least Squares (ALS) algorithm, and is computationally efficient and scalable. Furthermore, we establish the consistency of the change-point estimator under a set of general conditions. Simulations and empirical studies illustrate the validity and effectiveness.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"228 ","pages":"Article 110563"},"PeriodicalIF":0.7,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222582","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}

{"title":"Double dipping with balanced sampling","authors":"Blair Robertson,&nbsp;Chris Price,&nbsp;Marco Reale","doi":"10.1016/j.spl.2025.110562","DOIUrl":"10.1016/j.spl.2025.110562","url":null,"abstract":"<div><div>Doubly balanced samples from spatial populations have approximate balance on auxiliary variables and spread over spatial coordinates. This article shows that doubly balanced sampling is also efficient on non-spatial populations when we balance on auxiliary variables and spread over the space spanned by them. Numerical results on three example applications show that our extension of doubly balanced sampling works well in practice.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"228 ","pages":"Article 110562"},"PeriodicalIF":0.7,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145160357","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}

{"title":"Uniform mean estimation for monotonic processes","authors":"Eugenio Clerico ,&nbsp;Hamish E. Flynn ,&nbsp;Patrick Rebeschini","doi":"10.1016/j.spl.2025.110558","DOIUrl":"10.1016/j.spl.2025.110558","url":null,"abstract":"<div><div>We consider the problem of deriving uniform confidence bands for the mean of a monotonic stochastic process, such as the cumulative distribution function (CDF) of a random variable, based on a sequence of i.i.d. observations. Our approach leverages the coin-betting framework, and inherits several favourable characteristics of coin-betting methods. In particular, for each point in the domain of the mean function, we obtain anytime-valid confidence intervals that are numerically tight and adapt to the variance of the observations. To derive uniform confidence bands, we employ a continuous union bound that crucially leverages monotonicity. In the case of CDF estimation, we also exploit the fact that the empirical CDF is piece-wise constant to obtain simple confidence bands that can be easily computed. In simulations, we find that our confidence bands for the CDF achieve state-of-the-art performance.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"228 ","pages":"Article 110558"},"PeriodicalIF":0.7,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145160353","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}

{"title":"The eschewed sinh-arcsinh t distribution","authors":"M.C. Jones ,&nbsp;Arthur Pewsey","doi":"10.1016/j.spl.2025.110560","DOIUrl":"10.1016/j.spl.2025.110560","url":null,"abstract":"<div><div>Rosco et al. (2011) introduced and studied the sinh-arcsinh <span><math><mi>t</mi></math></span> (SAS-<span><math><mi>t</mi></math></span>) distribution. In this article, we introduce a modified version of that distribution which we call the eschewed sinh-arcsinh <span><math><mi>t</mi></math></span> (ESAS-<span><math><mi>t</mi></math></span>) distribution. The new proposal proves to be somewhat simpler than the former and, on balance, given the pros and cons listed in the article, we now recommend the ESAS-<span><math><mi>t</mi></math></span> distribution over the SAS-<span><math><mi>t</mi></math></span> distribution as the preferable version of a sinh-arcsinh <span><math><mi>t</mi></math></span> distribution.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"228 ","pages":"Article 110560"},"PeriodicalIF":0.7,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222581","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}

{"title":"A note on the structure of the filtering recursion for finite HMMs","authors":"Dimitrios Katselis ,&nbsp;Boris I. Godoy ,&nbsp;Rodrigo Carvajal ,&nbsp;Juan C. Agüero","doi":"10.1016/j.spl.2025.110556","DOIUrl":"10.1016/j.spl.2025.110556","url":null,"abstract":"<div><div>The filter for a finite HMM at time <span><math><mi>k</mi></math></span> is expressed in terms of a stochastic matrix <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span>. We relate arbitrary pairs of rows in <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span> with the corresponding pairs of rows in the underlying <span><math><mrow><mo>(</mo><mi>k</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></math></span>-step transition matrix <span><math><mrow><msup><mrow><mi>P</mi></mrow><mrow><mrow><mo>(</mo><mi>k</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></mrow></msup><mo>=</mo><msup><mrow><mi>P</mi></mrow><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msup></mrow></math></span>.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"228 ","pages":"Article 110556"},"PeriodicalIF":0.7,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145160358","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}

{"title":"Optimal sub-Gaussian variance proxy for truncated Gaussian and exponential random variables","authors":"Mathias Barreto ,&nbsp;Olivier Marchal ,&nbsp;Julyan Arbel","doi":"10.1016/j.spl.2025.110555","DOIUrl":"10.1016/j.spl.2025.110555","url":null,"abstract":"<div><div>This paper establishes the optimal sub-Gaussian variance proxy for truncated Gaussian and truncated exponential random variables. The proofs are based initially on reducing each distribution to their standardized versions. Geometrically, for the normal distribution, our argument consists of fitting a parabola to another parabola-looking function, which emerges from its moment generating function. For the exponential case, we show that the optimal variance proxy is the unique solution to a pair of equations and then provide this solution explicitly. Moreover, we demonstrate that truncated Gaussian variables exhibit strict sub-Gaussian behavior if and only if they are symmetric, meaning their truncation is symmetric with respect to the mean. Conversely, truncated exponential variables are shown to never exhibit strict sub-Gaussianity.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"228 ","pages":"Article 110555"},"PeriodicalIF":0.7,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145120274","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}

{"title":"Multiple testing in generalized universal inference","authors":"Neil Dey,&nbsp;Ryan Martin,&nbsp;Jonathan P. Williams","doi":"10.1016/j.spl.2025.110559","DOIUrl":"10.1016/j.spl.2025.110559","url":null,"abstract":"<div><div>Compared to p-values, e-values provably guarantee safe, valid inference. Applications often require consideration of multiple hypotheses simultaneously, and tools for handling such cases using e-values can be found in the relevant literature. Standard e-value constructions, however, require distributional assumptions that may not be justifiable. This short paper demonstrates that, depending on the multiple testing context, the generalized universal inference framework is well-suited for use with the existing e-value merging and adjustment strategies to control frequentist error rates in multiple testing when the quantities of interest are minimizers of risk functions, thereby avoiding the need for certain distributional assumptions. We demonstrate the strong performance of this general approach in a simulation study involving significance testing in quantile regression.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"228 ","pages":"Article 110559"},"PeriodicalIF":0.7,"publicationDate":"2025-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222579","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}

{"title":"On the product of correlated normal random variables and the noncentral chi-square difference distribution","authors":"Robert E. Gaunt","doi":"10.1016/j.spl.2025.110554","DOIUrl":"10.1016/j.spl.2025.110554","url":null,"abstract":"<div><div>We represent the product of two correlated normal random variables, and more generally the sum of independent copies of such random variables, as a difference of two independent noncentral chi-square random variables (which we refer to as the noncentral chi-square difference distribution). As a consequence, we obtain, amongst other results, an exact formula for the probability density function of the noncentral chi-square difference distribution, a Stein characterisation of the noncentral chi-square difference distribution, a simple formula for the moments of the sum of independent copies of the product of correlated normal random variables, an exact formula for the probability that such a random variable is negative, and also show that such random variables are self-decomposable and provide a Lévy–Khintchine representation of the characteristic function.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110554"},"PeriodicalIF":0.7,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046175","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}

{"title":"Parameter estimation of Burgers equations driven by white-colored noise","authors":"Yiming Jiang ,&nbsp;Yujue Wang ,&nbsp;Jie Xue","doi":"10.1016/j.spl.2025.110553","DOIUrl":"10.1016/j.spl.2025.110553","url":null,"abstract":"<div><div>In this paper, we study the stochastic generalized Burgers equation driven by a white-colored noise with the <span><math><mi>α</mi></math></span>-order heat kernel. First we construct a parametric estimator of the drift parameter through temporal quadratic variation of the solution. Then we obtain the consistency and convergence rate of the estimator.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110553"},"PeriodicalIF":0.7,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046179","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}