{"title":"Semistable distributions as marginals of operator stable laws","authors":"P. Kern , H.-P. Scheffler","doi":"10.1016/j.spl.2025.110458","DOIUrl":"10.1016/j.spl.2025.110458","url":null,"abstract":"<div><div>An example of Meerschaert (1990) shows that univariate marginals of an operator stable distribution are not necessarily stable distributions, but turned out to be semistable as shown by Meerschaert and Scheffler (1999). We characterize all semistable distributions that can appear as an univariate marginal of an operator stable law in terms of the spectral measure.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"226 ","pages":"Article 110458"},"PeriodicalIF":0.9,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144204528","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":"Asymptotic properties of goodness of fit tests based on higher order overlapping spacings","authors":"Sherzod M. Mirakhmedov","doi":"10.1016/j.spl.2025.110461","DOIUrl":"10.1016/j.spl.2025.110461","url":null,"abstract":"<div><div>The paper is devoted to tests for uniformity based on sum-functions of overlapping spacings, where the order of spacings can diverge to infinity as the sample size increases. In particular, it is shown that the asymptotic local power and Pitman asymptotic relative efficiencies of these tests depend significantly on the asymptotic properties of the counterpart statistics based on disjoint spacings. The general results are applied to a family of tests based on power divergence statistics.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"225 ","pages":"Article 110461"},"PeriodicalIF":0.9,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144190298","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":"Simplified k-sample nonparametric hypothesis tests for quantile residual event times","authors":"Nathan T. Provost, Abdus S. Wahed","doi":"10.1016/j.spl.2025.110463","DOIUrl":"10.1016/j.spl.2025.110463","url":null,"abstract":"<div><div>We present an approachable multi-sample hypothesis testing procedure for examining potential differences in quantile residual event times across an arbitrary number of groups. Moreover, an ancillary testing procedure that allows for the identification of group-specific significance with respect to a prespecified baseline group is also provided. Our simulations yield desirable power and type I error results when the chosen sample sizes accommodate the extremity of selected baseline values and quantiles of interest.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"225 ","pages":"Article 110463"},"PeriodicalIF":0.9,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144178553","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":"Superquantile function of order n and their applications in reliability and entropy","authors":"N. Unnikrishnan Nair , S.M. Sunoj , Silpa Subhash","doi":"10.1016/j.spl.2025.110457","DOIUrl":"10.1016/j.spl.2025.110457","url":null,"abstract":"<div><div>The superquantile function enjoys many more desirable properties than the conventional quantile function and as such may be considered as an alternative to the distribution function in probability calculus. It is expressed in terms of the mean life function and is used iteratively to construct a hierarchy of quantile functions. The sequence of the quantile function so obtained is used to develop the characterization results. The implications of the superquantile function in the context of explaining the vitality of an organism or unit are exploited to find the application to reliability analysis. Some applications to analysing cumulative residual entropy are also discussed.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"225 ","pages":"Article 110457"},"PeriodicalIF":0.9,"publicationDate":"2025-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144167409","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":"Submersion of a Markov process","authors":"Paul Nekoranik","doi":"10.1016/j.spl.2025.110456","DOIUrl":"10.1016/j.spl.2025.110456","url":null,"abstract":"<div><div>This note describes the transformation of a particular Gaussian process in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> by a submersion to <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>. The resulting process <span><math><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></mrow></math></span> is a time-homogeneous Markovian martingale for which <span><math><mrow><mo>(</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>,</mo><msub><mrow><mi>y</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>)</mo></mrow></math></span> is Gaussian for every <span><math><mrow><mi>t</mi><mo>></mo><mn>0</mn></mrow></math></span> and the covariance matrix of <span><math><mrow><mo>(</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>,</mo><msub><mrow><mi>y</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>)</mo></mrow></math></span> is exponentially increasing in <span><math><mi>t</mi></math></span>.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"225 ","pages":"Article 110456"},"PeriodicalIF":0.9,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144134956","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}
Saptati Datta, Riana Guha, Rachael Shudde, Valen E. Johnson
{"title":"Correction to “Bayes factors functions based on test statistics and non-local moment prior densities” [Statist. Probab. Lett. 219 (2025) 110330]","authors":"Saptati Datta, Riana Guha, Rachael Shudde, Valen E. Johnson","doi":"10.1016/j.spl.2025.110446","DOIUrl":"10.1016/j.spl.2025.110446","url":null,"abstract":"<div><div>We provide a correction to an equation in Table 1 of Datta et al. (2025) for two-sided t tests, as well as to the corresponding equation in the supplement that led to the error.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"224 ","pages":"Article 110446"},"PeriodicalIF":0.9,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144138924","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":"3 × 3 optimal ranked set sampling design with k cycles and best linear invariant estimators of the parameters for normal distribution","authors":"Minmin Li, Wangxue Chen","doi":"10.1016/j.spl.2025.110455","DOIUrl":"10.1016/j.spl.2025.110455","url":null,"abstract":"<div><div>In statistical parameter estimation problems, how well the parameters are estimated largely depends on the sampling design used. Cost effective sampling will be an important research problem. In this article, we find a 3 × 3 optimal ranked set sampling (RSS) design with <span><math><mi>k</mi></math></span> cycles for the normal distribution <span><math><mrow><mi>N</mi><mrow><mo>(</mo><mi>μ</mi><mo>,</mo><msup><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> in which the location parameter <span><math><mi>μ</mi></math></span> and the scale parameter <span><math><mi>σ</mi></math></span> are both unknown based on the D–optimal criterion in the experimental design. Then, the best linear invariant estimates (BLIEs) of <span><math><mi>μ</mi></math></span> and <span><math><mi>σ</mi></math></span> from <span><math><mrow><mi>N</mi><mrow><mo>(</mo><mi>μ</mi><mo>,</mo><msup><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> and their properties are studied under this RSS design. The efficiency is compared by the determinant of the mean square error matrix. The theoretical results and numerical results show that the BLIEs under the optimal RSS are more effective than the BLIEs under the balanced RSS.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"224 ","pages":"Article 110455"},"PeriodicalIF":0.9,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143948240","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 simple bootstrap method for large entropy unequal probability sampling designs","authors":"Yves Tillé","doi":"10.1016/j.spl.2025.110442","DOIUrl":"10.1016/j.spl.2025.110442","url":null,"abstract":"<div><div>We propose a simple bootstrap method for large entropy unequal probability sampling designs for finite populations. The method belongs to the class of bootstrap techniques that generate replication weights directly for the sampled units. It produces integer replication weights and is applicable to both equal and unequal probability designs characterized by high entropy, such as randomized systematic, pivotal, and maximum entropy designs. Our approach relies on the Dirichlet-Multinomial distribution to generate bootstrap samples while ensuring desirable statistical properties. We provide an efficient implementation in <span>R</span> and validate the method through simulations using real-world data. Results show that the proposed bootstrap estimator performs comparably to established variance estimation techniques while offering greater flexibility for non-linear estimators.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"224 ","pages":"Article 110442"},"PeriodicalIF":0.9,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143931544","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":"Construction of mixed-level column-orthogonal strong orthogonal arrays of strength two plus","authors":"Chen Li, Yan Zhu, Shanqi Pang","doi":"10.1016/j.spl.2025.110447","DOIUrl":"10.1016/j.spl.2025.110447","url":null,"abstract":"<div><div>Strong orthogonal arrays were introduced and studied as a class of space-filling designs for computer experiments. Column orthogonality is an important property in computer experiments. In this paper, using generalized multiplication, we introduce a new general method for obtaining mixed-level column-orthogonal strong orthogonal arrays (OSOAs) of strength two plus. We also use generator matrices and the expansive replacement method to obtain numerous new mixed-level OSOAs of strength two plus. The constructions offer convenience and flexibility in selecting factor levels and run sizes. As an application of these methods, the constructed OSOAs contain nearly all existing array classes as special cases. Some selective OSOAs are tabulated for practical uses.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"224 ","pages":"Article 110447"},"PeriodicalIF":0.9,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143929513","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 simplified condition for quantile regression","authors":"Liang Peng , Yongcheng Qi","doi":"10.1016/j.spl.2025.110444","DOIUrl":"10.1016/j.spl.2025.110444","url":null,"abstract":"<div><div>Quantile regression is effective in modeling and inferring the conditional quantile given some predictors and has become popular in risk management due to wide applications of quantile-based risk measures. When forecasting risk for economic and financial variables, quantile regression has to account for heteroscedasticity, which raises the question of whether the identification condition on residuals in quantile regression is equivalent to one independent of heteroscedasticity. In this paper, we present some identification conditions under three probability models and use them to establish simplified conditions in quantile regression.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"224 ","pages":"Article 110444"},"PeriodicalIF":0.9,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143899658","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}