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The averaging principle of Hilfer fractional stochastic pantograph equations with non-Lipschitz conditions 具有非 Lipschitz 条件的 Hilfer 分数随机受电弓方程的平均原理
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-08-02 DOI: 10.1016/j.spl.2024.110221
Ramkumar Kasinathan , Ravikumar Kasinathan , Dimplekumar Chalishajar , Dumitru Baleanu , Varshini Sandrasekaran
{"title":"The averaging principle of Hilfer fractional stochastic pantograph equations with non-Lipschitz conditions","authors":"Ramkumar Kasinathan ,&nbsp;Ravikumar Kasinathan ,&nbsp;Dimplekumar Chalishajar ,&nbsp;Dumitru Baleanu ,&nbsp;Varshini Sandrasekaran","doi":"10.1016/j.spl.2024.110221","DOIUrl":"10.1016/j.spl.2024.110221","url":null,"abstract":"<div><p>This paper is devoted to presenting an averaging principle for Hilfer fractional stochastic differential pantograph equations (HFSDPEs). The probability of the solutions to averaged stochastic systems in the means square sence can be used to approximate the solutions to HFSDPEs under appropriate non-Lipschitz conditions. Furthermore, certain previous results have been significantly generalised by our results. Finally, an example is given to demonstrate the feasibility of the results.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141940536","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
D-optimal designs for a multidimensional second-degree polynomial model with no intercept [省略公式]--无截距多维二级多项式模型的优化设计
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-07-31 DOI: 10.1016/j.spl.2024.110228
P.V. Shpilev
{"title":"D-optimal designs for a multidimensional second-degree polynomial model with no intercept","authors":"P.V. Shpilev","doi":"10.1016/j.spl.2024.110228","DOIUrl":"10.1016/j.spl.2024.110228","url":null,"abstract":"<div><p>The paper investigates the problem of constructing <span><math><mi>D</mi></math></span>-optimal designs for the multidimensional second-degree polynomial model without an intercept term. On a hyperparallelepiped of the given dimensionality and symmetric with respect to the origin, <span><math><mi>D</mi></math></span>-optimal designs are found in explicit analytical form.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141940480","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
Euler–Maruyama scheme for SDE driven by Lévy process with Hölder drift 具有赫尔德漂移的莱维过程驱动的 SDE 的 Euler-Maruyama 方案
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-07-27 DOI: 10.1016/j.spl.2024.110220
Yanfang Li, Guohuan Zhao
{"title":"Euler–Maruyama scheme for SDE driven by Lévy process with Hölder drift","authors":"Yanfang Li,&nbsp;Guohuan Zhao","doi":"10.1016/j.spl.2024.110220","DOIUrl":"10.1016/j.spl.2024.110220","url":null,"abstract":"<div><p>This study focuses on approximating solutions to SDEs driven by Lévy processes with Hölder continuous drifts using the Euler–Maruyama scheme. We derive the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-error for a broad range of driven noises, including all nondegenerate <span><math><mi>α</mi></math></span>-stable processes (<span><math><mrow><mn>0</mn><mo>&lt;</mo><mi>α</mi><mo>&lt;</mo><mn>2</mn></mrow></math></span>).</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141940481","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
Empirical limit theorems for Wiener chaos 维纳混沌的经验极限定理
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-07-27 DOI: 10.1016/j.spl.2024.110222
Shuyang Bai, Jiemiao Chen
{"title":"Empirical limit theorems for Wiener chaos","authors":"Shuyang Bai,&nbsp;Jiemiao Chen","doi":"10.1016/j.spl.2024.110222","DOIUrl":"10.1016/j.spl.2024.110222","url":null,"abstract":"<div><p>We consider empirical measures in a triangular array setup with underlying distributions varying as sample size grows. We study asymptotic properties of multiple integrals with respect to normalized empirical measures. Limit theorems involving series of multiple Wiener–Itô integrals are established.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141940539","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
Adaptive rank-based tests for high dimensional mean problems 针对高维均值问题的自适应秩检验
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-07-26 DOI: 10.1016/j.spl.2024.110226
Yu Zhang, Long Feng
{"title":"Adaptive rank-based tests for high dimensional mean problems","authors":"Yu Zhang,&nbsp;Long Feng","doi":"10.1016/j.spl.2024.110226","DOIUrl":"10.1016/j.spl.2024.110226","url":null,"abstract":"<div><p>The Wilcoxon signed-rank test and the Wilcoxon–Mann–Whitney test are commonly employed in one sample and two sample mean tests for one-dimensional hypothesis problems. For high-dimensional mean test problems, we calculate the asymptotic distribution of the maximum of rank statistics for each variable and suggest a max-type test. This max-type test is then merged with a sum-type test, based on their asymptotic independence offered by stationary and strong mixing assumptions. Our numerical studies reveal that this combined test demonstrates robustness and superiority over other methods, especially for heavy-tailed distributions.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141940534","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
Some new families of asymmetric nested orthogonal arrays with any strength 具有任意强度的非对称嵌套正交阵列的一些新系列
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-07-26 DOI: 10.1016/j.spl.2024.110219
Shanqi Pang, Yan Zhu, Xiao Lin
{"title":"Some new families of asymmetric nested orthogonal arrays with any strength","authors":"Shanqi Pang,&nbsp;Yan Zhu,&nbsp;Xiao Lin","doi":"10.1016/j.spl.2024.110219","DOIUrl":"10.1016/j.spl.2024.110219","url":null,"abstract":"<div><p>We propose a general method for constructing asymmetric nested orthogonal arrays (NOAs) with any strength via a newly defined matrix operation. The NOAs obtained can recursively produce other new NOAs. A lot of selective new asymmetric NOAs are tabulated.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141851683","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
Stackelberg differential reinsurance and investment game for a dependent risk model with Ornstein–Uhlenbeck process 具有奥恩斯坦-乌伦贝克过程的依赖风险模型的堆叠尔伯格差分再保险和投资博弈
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-07-25 DOI: 10.1016/j.spl.2024.110223
Yawen Zhang, Caibin Zhang
{"title":"Stackelberg differential reinsurance and investment game for a dependent risk model with Ornstein–Uhlenbeck process","authors":"Yawen Zhang,&nbsp;Caibin Zhang","doi":"10.1016/j.spl.2024.110223","DOIUrl":"10.1016/j.spl.2024.110223","url":null,"abstract":"<div><p>This paper considers a reinsurance and investment problem under the Stackelberg differential game. It assumes that the insurer can purchase reinsurance and the claim businesses between the insurer and the reinsurer are correlated through common shock dependence, and both of them are allowed to invest in a common risky asset whose price follows an Ornstein–Uhlenbeck process. By the stochastic control theory, explicit expressions of the optimal controls and the value functions are obtained for both of the insurer and reinsurer. We show that the optimal reinsurance strategy is a constant, which is independent of the time and risk-free interest rate. We also show that compared with the independent model, the insurer will purchase less reinsurance and the reinsurer will increase the premium price under the dependent risk model.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141851702","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 the asymptotic properties of extreme values of discrete random variables 论离散随机变量极值的渐近特性
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-07-25 DOI: 10.1016/j.spl.2024.110224
Kateryna Akbash , Natalia Doronina , Ivan Matsak
{"title":"On the asymptotic properties of extreme values of discrete random variables","authors":"Kateryna Akbash ,&nbsp;Natalia Doronina ,&nbsp;Ivan Matsak","doi":"10.1016/j.spl.2024.110224","DOIUrl":"10.1016/j.spl.2024.110224","url":null,"abstract":"<div><p>The article examines the almost sure asymptotic behaviour of extreme values of discrete random variables. We consider the case of random variables whose tails of the distribution are close to the tails of the geometric distribution or decrease faster.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141841937","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
A stereographic test of spherical uniformity 球面均匀性的立体测试
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-07-24 DOI: 10.1016/j.spl.2024.110218
Alberto Fernández-de-Marcos, Eduardo García-Portugués
{"title":"A stereographic test of spherical uniformity","authors":"Alberto Fernández-de-Marcos,&nbsp;Eduardo García-Portugués","doi":"10.1016/j.spl.2024.110218","DOIUrl":"10.1016/j.spl.2024.110218","url":null,"abstract":"<div><p>We introduce a test of uniformity for (hyper)spherical data motivated by the stereographic projection. The closed-form expression of the test statistic and its null asymptotic distribution are derived using Gegenbauer polynomials. The power against rotationally symmetric local alternatives is provided, and simulations illustrate the non-null asymptotic results. The stereographic test outperforms other tests in a testing scenario with antipodal dependence between observations.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167715224001871/pdfft?md5=2e72a66e79aca9edb78a99076367cd08&pid=1-s2.0-S0167715224001871-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141940541","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 sparsity index in Poisson size-biased sampling: Algorithms for the optimal unbiased estimation from small samples 泊松大小偏置抽样中的稀疏指数：小样本无偏估计最优算法
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-07-17 DOI: 10.1016/j.spl.2024.110217
Laura Bondi , Marcello Pagano , Marco Bonetti
{"title":"The sparsity index in Poisson size-biased sampling: Algorithms for the optimal unbiased estimation from small samples","authors":"Laura Bondi ,&nbsp;Marcello Pagano ,&nbsp;Marco Bonetti","doi":"10.1016/j.spl.2024.110217","DOIUrl":"10.1016/j.spl.2024.110217","url":null,"abstract":"<div><p>If the probability that a statistical unit is sampled is proportional to a size variable, then size bias occurs. As an example, when sampling individuals from a population, larger households are overrepresented.</p><p>With size-biased sampling, caution must be applied in estimation. We propose two exact algorithms for the calculation of the uniformly minimum variance unbiased estimator for the sparsity index in size-biased Poisson sampling. The algorithms are computationally burdensome even for small sample sizes, which is our setting of interest. As an alternative, a third, approximate algorithm based on the inverse Fourier transform is presented. We provide ready-to-use tables for the value of the optimal estimator.</p><p>An exact confidence interval based on the optimal estimator is also proposed, and the performance of the estimation procedure is compared to classical maximum likelihood inference, both in terms of mean squared error and average coverage probability and width of the confidence intervals.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141852911","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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