Banu Baydil, Victor H. de la Peña, Haolin Zou, Heyuan Yao
{"title":"Unbiased estimation of the Gini coefficient","authors":"Banu Baydil, Victor H. de la Peña, Haolin Zou, Heyuan Yao","doi":"10.1016/j.spl.2025.110376","DOIUrl":"10.1016/j.spl.2025.110376","url":null,"abstract":"<div><div>The Gini coefficient is a fundamental statistical measure of dispersion used widely across multiple fields. The interest in the study of the properties of the Gini coefficient is highlighted by the fact that every year the World Bank ranks the level of income inequality between countries using it. In order to calculate the coefficient, it is common practice to assume a Gamma-distributed set of values when modeling the dispersion of individual incomes in a given population. The asymptotic behavior of the sample Gini coefficient for populations following a Gamma distribution has been well-documented in the literature. However, research on the finite sample behavior has been absent due to the challenge posed by the denominator. This study aims to fill this gap by demonstrating theoretically that the sample Gini coefficient is an unbiased estimator of the population Gini coefficient for a population having Gamma (<span><math><mi>α</mi></math></span>, <span><math><mi>β</mi></math></span>) distribution. Furthermore, our result provides a way to quantify the downward bias due to grouping when the population Gini coefficient is estimated using the sample Gini coefficient of equal-sized groups.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"222 ","pages":"Article 110376"},"PeriodicalIF":0.9,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143529858","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":"Deviation inequalities for the spectral norm of structured random matrices","authors":"Guozheng Dai, Zhonggen Su","doi":"10.1016/j.spl.2025.110378","DOIUrl":"10.1016/j.spl.2025.110378","url":null,"abstract":"<div><div>We study the deviation inequality for the spectral norm of structured random matrices with non-gaussian entries. In particular, we establish an optimal bound for the <span><math><mi>p</mi></math></span>-th moment of the spectral norm by transfering the spectral norm into the suprema of canonical processes. A crucial ingredient of our proof is a comparison of weak and strong moments. As an application, we show a deviation inequality for the smallest singular value of a rectangular random matrix.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"221 ","pages":"Article 110378"},"PeriodicalIF":0.9,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143422061","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 increments of some extensions of the fractional Brownian motion","authors":"Charles El-Nouty","doi":"10.1016/j.spl.2025.110381","DOIUrl":"10.1016/j.spl.2025.110381","url":null,"abstract":"<div><div>Let <span><math><mrow><mo>{</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>H</mi></mrow></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>≥</mo><mn>0</mn><mo>}</mo></mrow></math></span> be a fractional Brownian motion with Hurst index <span><math><mrow><mn>0</mn><mo><</mo><mi>H</mi><mo><</mo><mn>1</mn></mrow></math></span>. Given that the process <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>H</mi></mrow></msub></math></span> has stationary increments, a detailed understanding of the characteristics of small, medium, and large increments is essential. This exploration extends to the QHASI class presented as a collection of centered Gaussian processes. This class is mainly characterized by a self-similarity, a quasi-helix and an approximately stationary increments assumptions. However, the analysis of these increments requires a different approach when considering the new extension of <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>H</mi></mrow></msub></math></span> proposed in some previous research. This investigation reveals significant differences in the behavior of increments within this extended framework.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"221 ","pages":"Article 110381"},"PeriodicalIF":0.9,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143421508","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":"Propagation of chaos for mean-field reflected BSDEs with jumps","authors":"Yiqing Lin , Kun Xu","doi":"10.1016/j.spl.2025.110382","DOIUrl":"10.1016/j.spl.2025.110382","url":null,"abstract":"<div><div>In this paper, we study a class of mean-field reflected backward stochastic differential equations (MF-RBSDEs) driven by a marked point process and also analyze MF-RBSDEs driven by a Poisson process. Based on a <span><math><mi>g</mi></math></span>-expectation representation lemma, we establish the existence and uniqueness of the particle system of MF-RBSDEs driven by a marked point process under Lipschitz generator conditions and obtain a convergence result of this system. In the Poisson setting, we obtain furthermore the convergence rate of the corresponding particle system toward the solution to the MF-RBSDEs driven by a Poisson process under bounded terminals and bounded obstacle conditions.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"221 ","pages":"Article 110382"},"PeriodicalIF":0.9,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143444808","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 oracle property of the generalized outcome-adaptive lasso","authors":"Ismaila Baldé","doi":"10.1016/j.spl.2025.110379","DOIUrl":"10.1016/j.spl.2025.110379","url":null,"abstract":"<div><div>The generalized outcome-adaptive lasso (GOAL) is a variable selection for high-dimensional causal inference proposed by Baldé et al. (2023). When the dimension is high, it is now well established that an ideal variable selection method should have the oracle property to ensure the optimal large sample performance. However, the oracle property of GOAL has not been proven. In this paper, we show that the GOAL estimator enjoys the oracle property. Our simulation shows that the GOAL method deals with the collinearity problem better than the oracle-like method, the outcome-adaptive lasso (OAL).</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"221 ","pages":"Article 110379"},"PeriodicalIF":0.9,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143422060","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}
Yiwei Shi , Huisheng Shu , Chunyang Wang , Xuekang Zhang
{"title":"Parameter estimation for Cox–Ingersoll–Ross process with two-sided reflections","authors":"Yiwei Shi , Huisheng Shu , Chunyang Wang , Xuekang Zhang","doi":"10.1016/j.spl.2024.110352","DOIUrl":"10.1016/j.spl.2024.110352","url":null,"abstract":"<div><div>In this paper, the least squares estimator (LSE) for the Cox–Ingersoll–Ross process with two-sided reflections is investigated on the basis of continuous observations. The strong consistency and asymptotic normality of LSE are derived. Computer simulations and empirical analysis are performed to illustrate our theory. Moreover, we also express the regulators using local time process.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"221 ","pages":"Article 110352"},"PeriodicalIF":0.9,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143421509","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 new maximum-type test for high-dimensional correlation matrices","authors":"Jing Chen , Ming Li , Kaige Zhao , Baisen Liu","doi":"10.1016/j.spl.2025.110365","DOIUrl":"10.1016/j.spl.2025.110365","url":null,"abstract":"<div><div>The exploration of the structure of high-dimensional correlation matrices has become an increasingly important topic in various fields. This paper aims to develop a novel method for testing the structure of high-dimensional correlation matrices. A new maximum-type test is proposed and the asymptotic distribution is derived, assuming that both the data dimension and the sample size tend towards infinity proportionally. Simulation studies show that our proposed test performs well for the sparse alternatives, dense alternatives, and a mixture of sparse and dense alternatives. Finally, the proposed method is employed to analyze a gene expression dataset.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"220 ","pages":"Article 110365"},"PeriodicalIF":0.9,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143360799","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":"Approximately mixing time series","authors":"Tim Kutta","doi":"10.1016/j.spl.2025.110360","DOIUrl":"10.1016/j.spl.2025.110360","url":null,"abstract":"<div><div>In this note, we present the new concept of approximate mixing for random variables on metric spaces. Approximate mixing is characterized by two constants <span><math><mrow><mi>ϵ</mi><mo>,</mo><mi>δ</mi><mo>≥</mo><mn>0</mn></mrow></math></span>, where <span><math><mi>ϵ</mi></math></span> is the mixing coefficient and <span><math><mi>δ</mi></math></span> is a slack variable. In the case <span><math><mrow><mi>δ</mi><mo>=</mo><mn>0</mn></mrow></math></span>, approximate mixing reduces to classical <span><math><mi>β</mi></math></span>-mixing. For positive slack, <span><math><mrow><mi>δ</mi><mo>></mo><mn>0</mn></mrow></math></span>, it becomes more general than traditional mixing assumptions, including important time series such as autoregressive processes on Hilbert spaces, that are generally not mixing. We prove that under approximate mixing analogous covariance inequalities hold as in the mixing case. We use these results to prove a central limit theorem for non-stationary time series on Hilbert spaces, which has potential applications in functional data analysis.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"220 ","pages":"Article 110360"},"PeriodicalIF":0.9,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143348646","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":"CellMCD+: An improved outlier-resistant cellwise minimum covariance determinant method","authors":"Prabhu Babu , Petre Stoica","doi":"10.1016/j.spl.2025.110366","DOIUrl":"10.1016/j.spl.2025.110366","url":null,"abstract":"<div><div>In this letter, we revisit the recently proposed cell outlier-resistant method cellMCD (minimum covariance determinant) and derive a version of it called cellMCD+ that has better performance. We illustrate the performance gain of cellMCD+ via numerical simulations in the case of estimating low-rank structured covariance matrices.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"220 ","pages":"Article 110366"},"PeriodicalIF":0.9,"publicationDate":"2025-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143202388","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":"Properties of the generalized inverse Gaussian with applications to Monte Carlo simulation and distribution function evaluation","authors":"Víctor Peña , Michael Jauch","doi":"10.1016/j.spl.2025.110359","DOIUrl":"10.1016/j.spl.2025.110359","url":null,"abstract":"<div><div>We introduce two mixture representations for the generalized inverse Gaussian (GIG) distribution. One mixture representation expresses the GIG as a continuous mixture of inverse Gaussians. The other reveals a relationship between GIGs. These mixture representations lead to new sampling methods and an exact algorithm for evaluating the distribution function of the GIG for half-integer <span><math><mi>p</mi></math></span>.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"220 ","pages":"Article 110359"},"PeriodicalIF":0.9,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143135861","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
