{"title":"Asymptotic optimality of generalized cross validation and regularized Mallows model averaging","authors":"Chenchen Zou , Xin Li , Xinmin Li , Hua Liang","doi":"10.1016/j.spl.2025.110406","DOIUrl":"10.1016/j.spl.2025.110406","url":null,"abstract":"<div><div>We propose a modified generalized cross-validation model averaging procedure for weight choice and prove the asymptotic optimality of the resultant estimators in the squared loss sense under much weaker assumptions than those imposed in the literature. The proposed model averaging can be regarded as an <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-regularized Mallows model averaging with varying coefficients. Furthermore, we propose a GCV-adjusted Mallows model averaging that achieves a faster convergence rate towards the optimal loss compared to using generalized cross-validation model averaging or Mallows model averaging individually. The performance of the proposed estimators is thoroughly evaluated through numerical experiments.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"222 ","pages":"Article 110406"},"PeriodicalIF":0.9,"publicationDate":"2025-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143636523","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 partial sums and extreme order statistics of i.i.d. random variables","authors":"Jiacheng Ye, Xin Chen, Jinghong Xiao","doi":"10.1016/j.spl.2025.110405","DOIUrl":"10.1016/j.spl.2025.110405","url":null,"abstract":"<div><div>This paper proves several limit theorems for the joint version of partial sums and extreme order statistics. The obtained results extend those of Li et al. (2024) to the case where the random variables have infinite variances.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"222 ","pages":"Article 110405"},"PeriodicalIF":0.9,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143636524","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":"Strong convergence order for slow-fast SDEs in Hölder norm","authors":"Jicheng Liu, Guiling Long","doi":"10.1016/j.spl.2025.110398","DOIUrl":"10.1016/j.spl.2025.110398","url":null,"abstract":"<div><div>In this paper, we first derive a criterion for strong convergence in Hölder norm by the Garsia–Rodemich–Rumsey’s lemma. Then we apply the criterion to a class of stochastic differential equations with slow and fast time-scales, and deduce the averaging principle in Hölder norm using the technique of Poisson equation. As a byproduct, the strong convergence in sup-norm can be obtained.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"222 ","pages":"Article 110398"},"PeriodicalIF":0.9,"publicationDate":"2025-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143593021","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}
Ayed. R.A. Alanzi , Shokrya S. Alshqaq , Raouf Fakhfakh
{"title":"A characterization of the Wigner’s semicircle law","authors":"Ayed. R.A. Alanzi , Shokrya S. Alshqaq , Raouf Fakhfakh","doi":"10.1016/j.spl.2025.110397","DOIUrl":"10.1016/j.spl.2025.110397","url":null,"abstract":"<div><div>This paper present a new characterization of the Wigner’s semicircle law. Denote by <span><math><mi>P</mi></math></span> (respectively by <span><math><msub><mrow><mi>P</mi></mrow><mrow><mi>b</mi><mi>a</mi></mrow></msub></math></span>) the set of non-degenerate real probabilities (respectively, with one sided support boundary from above). For <span><math><mrow><mi>ν</mi><mo>∈</mo><mi>P</mi></mrow></math></span> and <span><math><mrow><mi>a</mi><mo>∈</mo><mi>R</mi></mrow></math></span>, consider the transformation of measure <span><math><mi>ν</mi></math></span>, denoted <span><math><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>a</mi></mrow></msub><mrow><mo>(</mo><mi>ν</mi><mo>)</mo></mrow></mrow></math></span>, defined by <span><math><mrow><msub><mrow><mi>F</mi></mrow><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>a</mi></mrow></msub><mrow><mo>(</mo><mi>ν</mi><mo>)</mo></mrow></mrow></msub><mrow><mo>(</mo><mi>w</mi><mo>)</mo></mrow><mo>=</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>ν</mi></mrow></msub><mrow><mo>(</mo><mi>w</mi><mo>−</mo><mi>a</mi><mo>)</mo></mrow><mo>+</mo><mi>a</mi><mo>,</mo></mrow></math></span> where <span><math><mrow><msub><mrow><mi>F</mi></mrow><mrow><mi>ν</mi></mrow></msub><mrow><mo>(</mo><mi>⋅</mi><mo>)</mo></mrow></mrow></math></span> is the inverse of the Cauchy–Stieltjes transformation of <span><math><mi>ν</mi></math></span>. On the other hand, let <span><math><mrow><msub><mrow><mi>F</mi></mrow><mrow><mo>+</mo></mrow></msub><mrow><mo>(</mo><mi>μ</mi><mo>)</mo></mrow><mo>=</mo><mrow><mo>{</mo><msubsup><mrow><mi>Q</mi></mrow><mrow><mi>l</mi></mrow><mrow><mi>μ</mi></mrow></msubsup><mrow><mo>(</mo><mi>d</mi><mi>x</mi><mo>)</mo></mrow><mo>:</mo><mspace></mspace><mi>l</mi><mo>∈</mo><mrow><mo>(</mo><msubsup><mrow><mi>m</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>μ</mi></mrow></msubsup><mo>,</mo><msubsup><mrow><mi>m</mi></mrow><mrow><mo>+</mo></mrow><mrow><mi>μ</mi></mrow></msubsup><mo>)</mo></mrow><mo>}</mo></mrow></mrow></math></span> be the (CSK) family induced by <span><math><mrow><mi>μ</mi><mo>∈</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>b</mi><mi>a</mi></mrow></msub></mrow></math></span> with finite first moment <span><math><msubsup><mrow><mi>m</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>μ</mi></mrow></msubsup></math></span>. Define a novel family of probabilities <span><math><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>a</mi></mrow></msub><mrow><mo>(</mo><msub><mrow><mi>F</mi></mrow><mrow><mo>+</mo></mrow></msub><mrow><mo>(</mo><mi>μ</mi><mo>)</mo></mrow><mo>)</mo></mrow><mo>=</mo><mrow><mo>{</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>a</mi></mrow></msub><mrow><mo>(</mo><msubsup><mrow><mi>Q</mi></mrow><mrow><mi>l</mi></mrow><mrow><mi>μ</mi></mrow></msubsup><mo>)</mo></mrow><mrow><mo>(</mo><mi>d</mi><mi>x</mi><mo>)</mo></mrow><mo>:</mo><mspace></mspace><mi>l</mi><mo>∈</mo><mrow><mo>(</mo><msubsup><mrow><mi>m</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>μ</mi></mrow></msubsup><mo>,</mo><msubsup><mrow><mi>m</mi></mrow><mro","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"222 ","pages":"Article 110397"},"PeriodicalIF":0.9,"publicationDate":"2025-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143619123","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 testing mean of high dimensional compositional data","authors":"Qianqian Jiang, Wenbo Li, Zeng Li","doi":"10.1016/j.spl.2025.110396","DOIUrl":"10.1016/j.spl.2025.110396","url":null,"abstract":"<div><div>We investigate one/two-sample mean tests for high-dimensional compositional data when the number of variables is comparable with the sample size, as commonly encountered in microbiome research. Existing methods mainly focus on max-type test statistics which are suitable for detecting sparse signals. However, in this paper, we introduce a novel approach using sum-type test statistics which are capable of detecting weak but dense signals. By establishing the asymptotic independence between the max-type and sum-type test statistics, we further propose a combined max-sum type test to cover both cases. We derived the asymptotic null distributions and power functions for these test statistics. Simulation studies and real data applications demonstrate the superiority of our max-sum type test statistics which exhibit robust performance regardless of data sparsity.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"222 ","pages":"Article 110396"},"PeriodicalIF":0.9,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143552614","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":"Precise quantile function estimation from the characteristic function","authors":"Gero Junike","doi":"10.1016/j.spl.2025.110395","DOIUrl":"10.1016/j.spl.2025.110395","url":null,"abstract":"<div><div>We provide theoretical error bounds for the accurate numerical computation of the quantile function given the characteristic function of a continuous random variable. We show theoretically and empirically that the numerical error of the quantile function is typically several orders of magnitude larger than the numerical error of the cumulative distribution function for probabilities close to zero or one. We introduce the COS method for computing the quantile function. This method converges exponentially when the density is smooth and has semi-heavy tails and all parameters necessary to tune the COS method are given explicitly. Finally, we numerically test our theoretical results on the normal-inverse Gaussian and the tempered stable distributions.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"222 ","pages":"Article 110395"},"PeriodicalIF":0.9,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143552517","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}
{"title":"A jackknife empirical likelihood ratio test for log-symmetric distributions","authors":"Ganesh Vishnu Avhad, Ananya Lahiri","doi":"10.1016/j.spl.2025.110394","DOIUrl":"10.1016/j.spl.2025.110394","url":null,"abstract":"<div><div>A nonparametric test for assessing log-symmetric distributions is proposed, including the jackknife empirical likelihood and adjusted jackknife empirical likelihood ratio tests. The asymptotic distribution of the test statistic has been derived as well. A comprehensive Monte Carlo simulation study shows that the proposed tests exhibit good power against various alternative distributions. Additionally, the method is demonstrated using two real data sets to highlight their practical applicability.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"222 ","pages":"Article 110394"},"PeriodicalIF":0.9,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143534703","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":"Explicit formulae for projectively transformed Cauchy distributions with applications","authors":"Paulo R.S. Mendonça, Ben Lundell","doi":"10.1016/j.spl.2025.110393","DOIUrl":"10.1016/j.spl.2025.110393","url":null,"abstract":"<div><div>Cauchy distributions are characterized as the unique class of continuous distributions invariant to projective transformations, and this result naturally extends to the vector- and matrix-valued cases. We introduce a parameterization of Cauchy distributions that leads to elementary formulae for the parameters of projectively transformed matrix-valued Cauchy random variables, and illustrate an application of this result to the classical computer-vision problem of triangulation.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"222 ","pages":"Article 110393"},"PeriodicalIF":0.9,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143576936","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":"Efficient sampling in disease surveillance through subpopulations: Sampling canaries in the coal mine","authors":"Ivo V. Stoepker","doi":"10.1016/j.spl.2025.110384","DOIUrl":"10.1016/j.spl.2025.110384","url":null,"abstract":"<div><div>We consider outbreak detection settings of endemic diseases where the population consists of subpopulations available for stratified surveillance. Rather than sampling uniformly across the population, one may elevate effectiveness of detection methodology by optimally choosing a sampling subpopulation. We show (under some assumptions) the relative sampling efficiency between two subpopulations is inversely proportional to the ratio of their baseline disease risks. This implies one can increase sampling efficiency by sampling from the subpopulation with higher baseline disease risk. Our results require careful treatment of power curves of exact binomial tests as a function of their sample size, which are non-monotonic due to the underlying discreteness. A case study of COVID-19 cases in the Netherlands illustrates our theoretical findings.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"222 ","pages":"Article 110384"},"PeriodicalIF":0.9,"publicationDate":"2025-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143552518","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}
{"title":"The Bahadur representation for sample quantiles of ρ-mixing random variables","authors":"Dagmara Dudek, Anna Kuczmaszewska","doi":"10.1016/j.spl.2025.110386","DOIUrl":"10.1016/j.spl.2025.110386","url":null,"abstract":"<div><div>In this paper we investigate the strong consistency and the Bahadur representation of sample quantiles for <span><math><mi>ρ</mi></math></span>-mixing random variables. Moreover, we prove the asymptotic normality and the Berry–Esseen bound of sample quantiles for <span><math><mi>ρ</mi></math></span>-mixing random variables. To illustrate the obtained results some numerical simulations are presented.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"221 ","pages":"Article 110386"},"PeriodicalIF":0.9,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143479553","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}
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
