Statistics & Probability Letters最新文献

{"title":"On the maximal correlation coefficient for the bivariate Marshall Olkin distribution","authors":"Axel Bücher,&nbsp;Torben Staud","doi":"10.1016/j.spl.2024.110323","DOIUrl":"10.1016/j.spl.2024.110323","url":null,"abstract":"<div><div>We prove a formula for the maximal correlation coefficient of the bivariate Marshall Olkin distribution that was conjectured in Lin et al., 2016. The formula is applied to obtain a new proof for a variance inequality in extreme value statistics that links the disjoint and the sliding block maxima method.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110323"},"PeriodicalIF":0.9,"publicationDate":"2024-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161005","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":"Geometric quantile-based measures of multivariate distributional characteristics","authors":"Ha-Young Shin,&nbsp;Hee-Seok Oh","doi":"10.1016/j.spl.2024.110325","DOIUrl":"10.1016/j.spl.2024.110325","url":null,"abstract":"<div><div>Several new geometric quantile-based measures for multivariate dispersion, skewness, kurtosis, and spherical asymmetry are defined. These measures differ from existing measures, which use volumes, and are easy to calculate. Some theoretical justification is given, followed by experiments illustrating that they are sensible measures of these distributional characteristics and some basic empirical justification for bootstrapped confidence regions.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110325"},"PeriodicalIF":0.9,"publicationDate":"2024-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162106","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":"Moderate deviations for the number of descents in a random permutation","authors":"Hui Jiang,&nbsp;Jing Wang","doi":"10.1016/j.spl.2024.110320","DOIUrl":"10.1016/j.spl.2024.110320","url":null,"abstract":"<div><div>The number of descents in a random permutation has close connections with generalized Pólya urn and random trees. Via the Laplace functional calculations and asymptotic analysis techniques, we prove that the number of descents satisfies the moderate deviations and Cramér type moderate deviations. Then, using the martingale difference representation, we establish the functional moderate deviations in <span><math><mrow><mi>D</mi><mrow><mo>(</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow><mo>,</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> equipped with the uniform topology.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110320"},"PeriodicalIF":0.9,"publicationDate":"2024-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162105","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":"New proofs to measurable, predictable and optional section theorems","authors":"Stefanos Theodorakopoulos","doi":"10.1016/j.spl.2024.110324","DOIUrl":"10.1016/j.spl.2024.110324","url":null,"abstract":"<div><div>We present new, short and elementary proofs of the famous section theorems that are used in Stochastic Calculus. Predictable section is proved directly while measurable section is a simple corollary. Then, optional (resp. accessible) section follows from an intuitive approximation argument based on the dichotomy of predictable and total inaccessible times.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110324"},"PeriodicalIF":0.9,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162108","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 first exit time of fractional Brownian motion from an unbounded domain","authors":"Yinbing Zhou,&nbsp;Dawei Lu","doi":"10.1016/j.spl.2024.110319","DOIUrl":"10.1016/j.spl.2024.110319","url":null,"abstract":"<div><div>Consider a fractional Brownian motions starting at the interior point <span><math><mrow><mfenced><mrow><msub><mrow><mi>x</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><mi>h</mi><mfenced><mrow><mo>‖</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>‖</mo></mrow></mfenced><mo>+</mo><mn>2</mn><mi>K</mi></mrow></mfenced><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msup></mrow></math></span> with the constant <span><math><mrow><mi>K</mi><mo>&gt;</mo><mn>1</mn></mrow></math></span>, for some fixed <span><math><mrow><msub><mrow><mi>x</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></mrow></math></span>, of an unbounded domain <span><math><mrow><mi>D</mi><mo>=</mo><mfenced><mrow><mfenced><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow></mfenced><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>:</mo><mi>y</mi><mo>&gt;</mo><mi>h</mi><mfenced><mrow><mo>‖</mo><mi>x</mi><mo>‖</mo></mrow></mfenced></mrow></mfenced></mrow></math></span>, The function <span><math><mi>h</mi></math></span> is a nondecreasing, lower semicontinuous, and convex function on <span><math><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow></math></span> with <span><math><mrow><mi>h</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></mrow></math></span> being finite. Here we take <span><math><mrow><msup><mrow><mi>h</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mfenced><mrow><mi>x</mi></mrow></mfenced><mo>=</mo><mi>A</mi><msup><mrow><mi>x</mi></mrow><mrow><mi>α</mi></mrow></msup><msup><mrow><mfenced><mrow><mo>log</mo><mi>x</mi></mrow></mfenced></mrow><mrow><mi>β</mi></mrow></msup></mrow></math></span>with a positive constant <span><math><mi>A</mi></math></span> for <span><math><mrow><mi>x</mi><mo>&gt;</mo><mi>K</mi></mrow></math></span>. It is evident that <span><math><mrow><msup><mrow><mi>h</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> exhibits monotonic behavior for sufficiently large values of <span><math><mi>x</mi></math></span>. Let <span><math><msub><mrow><mi>τ</mi></mrow><mrow><mi>D</mi></mrow></msub></math></span> denote the first time that the fractional Brownian motion exits from <span><math><mi>D</mi></math></span>. In most cases, we give the asymptotically equivalent estimate of <span><math><mrow><mo>log</mo><mi>P</mi><mfenced><mrow><msub><mrow><mi>τ</mi></mrow><mrow><mi>D</mi></mrow></msub><mo>&gt;</mo><mi>t</mi></mrow></mfenced></mrow></math></span>. The proof methods are based on the earlier works of Li, Shi, Lifshits, and Aurzada.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"218 ","pages":"Article 110319"},"PeriodicalIF":0.9,"publicationDate":"2024-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143149205","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 split-plot designs under individual word length patterns","authors":"Xiaoxue Han ,&nbsp;Chong Sheng ,&nbsp;Min-Qian Liu","doi":"10.1016/j.spl.2024.110311","DOIUrl":"10.1016/j.spl.2024.110311","url":null,"abstract":"<div><div>For multi-factor experiments that cannot run all the factors in a completely random order, fractional factorial split-plot (FFSP) designs are often used in practice. When some prior knowledge has shown that some factors are more likely to be significant than others, Han et al. (2023) proposed the individual word length patterns (IWLPs) of whole-plot (WP) and sub-plot (SP), denoted by the I<span><math><msub><mrow></mrow><mrow><mi>w</mi></mrow></msub></math></span>WLP and I<span><math><msub><mrow></mrow><mrow><mi>s</mi></mrow></msub></math></span>WLP respectively, in the FFSP design. In this paper, we propose a construction method for optimal FFSP designs based on these two criteria, where the key of the method is to construct generating matrices for different FFSP designs from the generating matrix of a fractional factorial design, and hence we get a class of effective FFSP designs. These designs are more applicable in many situations. The results for 16-run two-level FFSP designs are tabulated in the supplementary material for possible use by practitioners.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110311"},"PeriodicalIF":0.9,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162107","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":"Semi-supervised estimation of a single-index varying-coefficient model","authors":"Peng Lai,&nbsp;Zhou Wang,&nbsp;Yurong Zhang","doi":"10.1016/j.spl.2024.110312","DOIUrl":"10.1016/j.spl.2024.110312","url":null,"abstract":"<div><div>We introduce a single-index varying-coefficient model for the Framingham heart disease data and propose a semi-supervised estimation method that effectively utilizes unlabeled data. The method outperforms traditional approaches in accuracy, as validated by simulations and real examples.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"218 ","pages":"Article 110312"},"PeriodicalIF":0.9,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142756828","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":"Berry–Esseen expansion and Cramér-type large deviation for run and tumble particles on one dimension","authors":"Wenxuan Chen,&nbsp;Zhi Qu","doi":"10.1016/j.spl.2024.110308","DOIUrl":"10.1016/j.spl.2024.110308","url":null,"abstract":"<div><div>In this paper, we consider the run and tumble particles on one-dimensional lattice <span><math><mi>Z</mi></math></span>. We derive Berry–Esseen bound for the active particle. Moreover, we also obtain the Cramér-type large deviation when the particle evolves on the discrete time set <span><math><mi>N</mi></math></span>.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"218 ","pages":"Article 110308"},"PeriodicalIF":0.9,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142744390","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":"Is the effective sample size always less than n? A spatial regression approach","authors":"Clemente Ferrer,&nbsp;Ronny Vallejos","doi":"10.1016/j.spl.2024.110309","DOIUrl":"10.1016/j.spl.2024.110309","url":null,"abstract":"<div><div>In this paper, within a spatial statistics framework, we present an upper bound for the effective sample size (ESS) as defined by Vallejos and Osorio (2014), addressing a research gap regarding the mathematical properties of the ESS. There are certain correlation structures for which the ESS exceeds <span><math><mi>n</mi></math></span>, which is inconsistent with the maximum possible sample size. Our approach identifies conditions on the correlation matrix of a spatial process that ensure that the equivalent number of independent and identically distributed observations within a spatial sample of size <span><math><mi>n</mi></math></span> does not exceed <span><math><mi>n</mi></math></span>. This property is desirable because it ensures the effectiveness of reduction measures.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"218 ","pages":"Article 110309"},"PeriodicalIF":0.9,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142744480","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":"Improving the Bickel–Rosenblatt global measure of deviation and goodness-of-fit test","authors":"S. Ejaz Ahmed ,&nbsp;Mohamed Amezziane ,&nbsp;Keshab Dahal","doi":"10.1016/j.spl.2024.110310","DOIUrl":"10.1016/j.spl.2024.110310","url":null,"abstract":"<div><div>We propose a zero-centered version of the Bickel–Rosenblatt statistic and use it to construct goodness of fit tests. We derive the null distributions and power functions of these tests along with their consistency results. A simulation study is carried out to show how the new tests outperform traditional ones.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"218 ","pages":"Article 110310"},"PeriodicalIF":0.9,"publicationDate":"2024-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143149200","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}