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FWER for normal distribution in nearly independent setup
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-12-19 DOI: 10.1016/j.spl.2024.110340
Nabaneet Das , Subir Kumar Bhandari
{"title":"FWER for normal distribution in nearly independent setup","authors":"Nabaneet Das ,&nbsp;Subir Kumar Bhandari","doi":"10.1016/j.spl.2024.110340","DOIUrl":"10.1016/j.spl.2024.110340","url":null,"abstract":"<div><div>Das and Bhandari (2021) demonstrated that the Family-Wise Error Rate (FWER) of Bonferroni procedure is asymptotically bounded by <span><math><mrow><mi>α</mi><mrow><mo>(</mo><mn>1</mn><mo>−</mo><mi>ρ</mi><mo>)</mo></mrow></mrow></math></span>, where <span><math><mi>ρ</mi></math></span> is the correlation among hypotheses and <span><math><mi>α</mi></math></span> is the significance level. Dey and Bhandari (2023) expanded on this by showing that, under equicorrelated normal distribution, the FWER approaches zero as the number of hypotheses increases. Their findings also reveal a key insight: while the FWER stays positive when there is no correlation, it asymptotically tends to zero with any non-zero correlation, indicating a discontinuity at <span><math><mrow><mi>ρ</mi><mo>=</mo><mn>0</mn></mrow></math></span>. This suggests the need to investigate how the FWER behaves as correlation coefficients approach zero. This paper aims to explore how closely the FWER of Bonferroni method resembles its behavior under independence and introduces an asymptotic correction factor to improve accuracy in nearly independent cases.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110340"},"PeriodicalIF":0.9,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161021","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 maximum overlap time in the M/M/1 queue
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-12-18 DOI: 10.1016/j.spl.2024.110322
Sergio Palomo , Jamol Pender
{"title":"The maximum overlap time in the M/M/1 queue","authors":"Sergio Palomo ,&nbsp;Jamol Pender","doi":"10.1016/j.spl.2024.110322","DOIUrl":"10.1016/j.spl.2024.110322","url":null,"abstract":"<div><div>In this paper, we analyze the steady state maximum overlap time in the M/M/1 queue. We derive the maximum overlap time tail distribution, its moments and the moment generating function. We also analyze the steady state minimum overlap time of the adjacent customers and compute its moments and moment generating function. Our results provide new insight on how customers become infected in the M/M/1 queue.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110322"},"PeriodicalIF":0.9,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143128509","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
On Stein factors in Stein’s method for normal approximation
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-12-14 DOI: 10.1016/j.spl.2024.110339
Robert E. Gaunt
{"title":"On Stein factors in Stein’s method for normal approximation","authors":"Robert E. Gaunt","doi":"10.1016/j.spl.2024.110339","DOIUrl":"10.1016/j.spl.2024.110339","url":null,"abstract":"<div><div>Building on the rather large literature concerning the regularity of the solution of the standard normal Stein equation, we provide a complete description of the best possible uniform bounds for the derivatives of the solution of the standard normal Stein equation when the test functions belong to the class of real-valued functions whose <span><math><mi>k</mi></math></span>th order derivative is Lipschitz.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110339"},"PeriodicalIF":0.9,"publicationDate":"2024-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161024","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
The method of moments for multivariate random sums in the Poisson-Skew-Normal case
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-12-13 DOI: 10.1016/j.spl.2024.110338
Farrukh Javed , Nicola Loperfido , Stepan Mazur
{"title":"The method of moments for multivariate random sums in the Poisson-Skew-Normal case","authors":"Farrukh Javed ,&nbsp;Nicola Loperfido ,&nbsp;Stepan Mazur","doi":"10.1016/j.spl.2024.110338","DOIUrl":"10.1016/j.spl.2024.110338","url":null,"abstract":"<div><div>Multivariate random sums appear in many scientific fields, most notably in actuarial science, where they model both the number of claims and their sizes. Unfortunately, they pose severe inferential problems. For example, their density function is analytically intractable, in the general case, thus preventing likelihood inference. In this paper, we address the problem by the method of moments, under the assumption that the claim size and the claim number have a multivariate skew-normal and a Poisson distribution, respectively. In doing so, we also derive closed-form expressions for some fundamental measures of multivariate kurtosis and highlight some limitations of both projection pursuit and invariant coordinate selection.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110338"},"PeriodicalIF":0.9,"publicationDate":"2024-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161026","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
Bayes factors functions based on test statistics and non-local moment prior densities
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-12-10 DOI: 10.1016/j.spl.2024.110330
Saptati Datta, Riana Guha, Rachael Shudde, Valen E. Johnson
{"title":"Bayes factors functions based on test statistics and non-local moment prior densities","authors":"Saptati Datta,&nbsp;Riana Guha,&nbsp;Rachael Shudde,&nbsp;Valen E. Johnson","doi":"10.1016/j.spl.2024.110330","DOIUrl":"10.1016/j.spl.2024.110330","url":null,"abstract":"<div><div>We describe Bayes factors based on <em>z</em>, <em>t</em>, <span><math><msup><mrow><mi>χ</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>, and <em>F</em> statistics when non-local moment prior distributions are used to define alternative hypotheses. The non-local alternative prior distributions are centered on standardized effects. The prior densities include a dispersion parameter that can be used to model prior precision and the variation of effect sizes across replicated experiments. We examine the convergence rates of Bayes factors under true null and true alternative hypotheses and show how these Bayes factors can be used to construct Bayes factor functions. Examples illustrate the application of resulting Bayes factors functions to psychological experiments.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110330"},"PeriodicalIF":0.9,"publicationDate":"2024-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162102","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
Transportation cost-information inequality for stochastic wave equation with spatially inhomogeneous white noise
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-12-06 DOI: 10.1016/j.spl.2024.110321
Zhigang Yao, Bin Zhang, Junfeng Liu
{"title":"Transportation cost-information inequality for stochastic wave equation with spatially inhomogeneous white noise","authors":"Zhigang Yao,&nbsp;Bin Zhang,&nbsp;Junfeng Liu","doi":"10.1016/j.spl.2024.110321","DOIUrl":"10.1016/j.spl.2024.110321","url":null,"abstract":"<div><div>In this paper, we prove the existence, uniqueness and Hölder continuity of the mild solution to the nonlinear stochastic wave equation driven by spatially inhomogeneous white noise. Furthermore, we establish a Talagrand’s <span><math><msub><mrow><mi>T</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> transportation cost-information inequality for the law of the solution on the continuous path space with respect to the weighted <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-metric.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110321"},"PeriodicalIF":0.9,"publicationDate":"2024-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161025","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
Stable approximation for call function via Stein’s method
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-12-05 DOI: 10.1016/j.spl.2024.110328
Peng Chen , Tianyi Qi , Ting Zhang
{"title":"Stable approximation for call function via Stein’s method","authors":"Peng Chen ,&nbsp;Tianyi Qi ,&nbsp;Ting Zhang","doi":"10.1016/j.spl.2024.110328","DOIUrl":"10.1016/j.spl.2024.110328","url":null,"abstract":"<div><div>Let <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> be a sum of independent identically distribution random variables with finite first moment and <span><math><msub><mrow><mi>h</mi></mrow><mrow><mi>M</mi></mrow></msub></math></span> be a call function defined by <span><math><mrow><msub><mrow><mi>g</mi></mrow><mrow><mi>M</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mo>max</mo><mrow><mo>{</mo><mi>x</mi><mo>−</mo><mi>M</mi><mo>,</mo><mn>0</mn><mo>}</mo></mrow></mrow></math></span> for <span><math><mrow><mi>x</mi><mo>∈</mo><mi>R</mi></mrow></math></span>, <span><math><mrow><mi>M</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>. In this paper, we assume the random variables are in the domain <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>α</mi></mrow></msub></math></span> of normal attraction of a stable law of exponent <span><math><mi>α</mi></math></span>, then for <span><math><mrow><mi>α</mi><mo>∈</mo><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span>, we use the Stein’s method developed in Chen et al. (2024) to give uniform and non uniform bounds on <span><math><mi>α</mi></math></span>-stable approximation for the call function without additional moment assumptions. These results will make the approximation theory of call function applicable to the lower moment conditions, and greatly expand the scope of application of call function in many fields.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110328"},"PeriodicalIF":0.9,"publicationDate":"2024-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162100","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
Limiting distribution for infinite-server batch service queues
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-12-05 DOI: 10.1016/j.spl.2024.110327
Bara Kim , Jeongsim Kim
{"title":"Limiting distribution for infinite-server batch service queues","authors":"Bara Kim ,&nbsp;Jeongsim Kim","doi":"10.1016/j.spl.2024.110327","DOIUrl":"10.1016/j.spl.2024.110327","url":null,"abstract":"<div><div>Nakamura and Phung-Duc (2023) conjectured that, for an infinite-server batch service queue with Poisson arrivals, the central limit theorem for the number of busy servers, conditioned on the number of waiting customers and the size of the batch to be served, holds as the arrival rate goes to infinity. In this paper, we resolve this conjecture using the theory of Markov regenerative processes and further extend the result to renewal arrival models.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110327"},"PeriodicalIF":0.9,"publicationDate":"2024-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162101","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
Kac’s central limit theorem by Stein’s method
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-12-05 DOI: 10.1016/j.spl.2024.110329
Suprio Bhar , Ritwik Mukherjee , Prathmesh Patil
{"title":"Kac’s central limit theorem by Stein’s method","authors":"Suprio Bhar ,&nbsp;Ritwik Mukherjee ,&nbsp;Prathmesh Patil","doi":"10.1016/j.spl.2024.110329","DOIUrl":"10.1016/j.spl.2024.110329","url":null,"abstract":"<div><div>In 1946, Mark Kac proved a Central Limit type theorem for a sequence of random variables that were not independent. The random variables under consideration were obtained from the angle-doubling map. The idea behind Kac’s proof was to show that although the random variables under consideration were not independent, they were what he calls <em>statistically independent</em> (in modern terminology, this concept is called long range independence). Using that observation, Kac showed that the sample averages of the random variables, suitably normalized, converges to the standard normal distribution. In this paper, we give a new proof of Kac’s result by applying Stein’s method. We show that the normalized sample averages converge to the standard normal distribution in the Wasserstein metric, which in particular implies convergence in distribution.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110329"},"PeriodicalIF":0.9,"publicationDate":"2024-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162103","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
Almost sure convergence of the waiting time for a G/G/1 queue in heavy traffic
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-12-04 DOI: 10.1016/j.spl.2024.110326
Ye Xia
{"title":"Almost sure convergence of the waiting time for a G/G/1 queue in heavy traffic","authors":"Ye Xia","doi":"10.1016/j.spl.2024.110326","DOIUrl":"10.1016/j.spl.2024.110326","url":null,"abstract":"<div><div>Consider a G/G/1 queueing model with traffic intensity <span><math><mrow><mi>ρ</mi><mo>=</mo><mn>1</mn></mrow></math></span>. Let <span><math><msub><mrow><mi>W</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> be the waiting time in the queue for customer <span><math><mi>n</mi></math></span>. We provide a class of sufficient conditions for almost sure convergence of <span><math><mrow><msub><mrow><mi>W</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>/</mo><msup><mrow><mi>n</mi></mrow><mrow><mi>α</mi></mrow></msup></mrow></math></span> to 0, where <span><math><mrow><mi>α</mi><mo>&gt;</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math></span>.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110326"},"PeriodicalIF":0.9,"publicationDate":"2024-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162104","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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