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Explicit bounds for a Gaussian decomposition Lemma of Sellke
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-12-30 DOI: 10.1016/j.spl.2024.110342
Tobias Schmidt
{"title":"Explicit bounds for a Gaussian decomposition Lemma of Sellke","authors":"Tobias Schmidt","doi":"10.1016/j.spl.2024.110342","DOIUrl":"10.1016/j.spl.2024.110342","url":null,"abstract":"<div><div>In <span><span>Sellke (2024)</span></span> a decomposition of Gaussian measures on finite dimensional spaces was introduced, which turned out to be a central technical tool to improve currently known bounds on a long standing conjecture in statistical mechanics called the Polaron problem. This note slightly generalizes this decomposition and provides numerical values for all occurring constants.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110342"},"PeriodicalIF":0.9,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161015","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
Two-barriers-reflected BSDE with rank-based data
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-12-28 DOI: 10.1016/j.spl.2024.110343
Xinwei Feng, Lu Wang
{"title":"Two-barriers-reflected BSDE with rank-based data","authors":"Xinwei Feng,&nbsp;Lu Wang","doi":"10.1016/j.spl.2024.110343","DOIUrl":"10.1016/j.spl.2024.110343","url":null,"abstract":"<div><div>We investigate two-barriers-reflected backward stochastic differential equations with data from rank-based stochastic differential equation. More specifically, we focus on the solution of backward stochastic differential equations restricted to two prescribed upper-boundary and lower-boundary processes. We rigorously show that this solution gives a probabilistic expression to the viscosity solution of some obstacle problems for the corresponding parabolic partial differential equations. As an application, the pricing problem of an American game option is studied.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110343"},"PeriodicalIF":0.9,"publicationDate":"2024-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161019","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 law of the iterated logarithm for functionals of the Wiener process
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-12-26 DOI: 10.1016/j.spl.2024.110341
A. Logachov , A. Yambartsev
{"title":"The law of the iterated logarithm for functionals of the Wiener process","authors":"A. Logachov ,&nbsp;A. Yambartsev","doi":"10.1016/j.spl.2024.110341","DOIUrl":"10.1016/j.spl.2024.110341","url":null,"abstract":"<div><div>In this note, we establish a law of the iterated logarithm for Fréchet differentiable functionals of a general form with respect to the Wiener process for a small time. The proof method shares conceptual similarities with the delta method.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110341"},"PeriodicalIF":0.9,"publicationDate":"2024-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161023","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
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
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