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On the representation and computational aspects of the distribution of a linear combination of independent noncentral chi-squared random variables 关于独立非中心秩方随机变量线性组合分布的表示和计算问题
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-11-01 DOI: 10.1016/j.spl.2024.110291
Alfred Kume , Tomonari Sei , Andrew T.A. Wood
{"title":"On the representation and computational aspects of the distribution of a linear combination of independent noncentral chi-squared random variables","authors":"Alfred Kume ,&nbsp;Tomonari Sei ,&nbsp;Andrew T.A. Wood","doi":"10.1016/j.spl.2024.110291","DOIUrl":"10.1016/j.spl.2024.110291","url":null,"abstract":"<div><div>This article presents two new results relevant to a linear combination of <span><math><msup><mrow><mi>χ</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> random variables. The first result expresses the cumulative distribution function as a simple multiple of a certain tilted density. The second result shows that in important cases the inversion integral for the density may be expressed as a sum of relatively simple real integrals which, using suitable numerical methods, are straightforward to compute quickly and accurately.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"218 ","pages":"Article 110291"},"PeriodicalIF":0.9,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142703929","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
Optimal tightening of the KWW joint confidence region for a ranking 优化收紧 KWW 联合置信区的排序
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-10-30 DOI: 10.1016/j.spl.2024.110288
Tommy Wright
{"title":"Optimal tightening of the KWW joint confidence region for a ranking","authors":"Tommy Wright","doi":"10.1016/j.spl.2024.110288","DOIUrl":"10.1016/j.spl.2024.110288","url":null,"abstract":"<div><div>Klein, Wright, and Wieczorek (2020), hereafter KWW, constructs a simple novel measure of uncertainty for an estimated ranking using a joint confidence region for the true ranking of <span><math><mi>K</mi></math></span> populations. In this current paper, our proposed framework permits some control over the amount of uncertainty and tightness in various portions of the estimated ranking with an optimal allocation of sample among the <span><math><mi>K</mi></math></span> populations.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"217 ","pages":"Article 110288"},"PeriodicalIF":0.9,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142651260","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 one-way MANOVA test for high-dimensional data using clustering subspaces 利用聚类子空间对高维数据进行单向 MANOVA 检验
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-10-29 DOI: 10.1016/j.spl.2024.110293
Minyuan Lu, Bu Zhou
{"title":"A one-way MANOVA test for high-dimensional data using clustering subspaces","authors":"Minyuan Lu,&nbsp;Bu Zhou","doi":"10.1016/j.spl.2024.110293","DOIUrl":"10.1016/j.spl.2024.110293","url":null,"abstract":"<div><div>This study focuses on the high-dimensional one-way analysis of variance problem, specifically, testing whether multiple population mean vectors are equal in the context of high-dimensional data. To solve the problem that classical multivariate analysis of variance (MANOVA) test statistics are undefined when the dimensionality surpasses the sample size, we propose a random permutation test using low-dimensional subspaces obtained by clustering of variables. The test statistics are derived from a one-way MANOVA decomposition for clustered variables and this approach utilizes the correlation information among variables to ensure high testing power. Simulation studies indicate that the proposed test performs well with high-dimensional data.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"217 ","pages":"Article 110293"},"PeriodicalIF":0.9,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142594045","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
Probability and moment inequalities for quadratic forms in independent random variables with fat tails 具有胖尾的独立随机变量中二次型的概率和矩不等式
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-10-28 DOI: 10.1016/j.spl.2024.110290
Chi Zhang, Danna Zhang
{"title":"Probability and moment inequalities for quadratic forms in independent random variables with fat tails","authors":"Chi Zhang,&nbsp;Danna Zhang","doi":"10.1016/j.spl.2024.110290","DOIUrl":"10.1016/j.spl.2024.110290","url":null,"abstract":"<div><div>Probability and moment inequalities for quadratic forms are valuable tools in studying the properties of second-order statistics. There are extensive results regarding quadratic forms in random variables with finite exponential moments. However, the counterpart that allows for weaker moment conditions is inadequate. In this work, we present a new Nagaev-type tail probability inequality and a Rosenthal-type moment inequality for quadratic forms in random variables with fat tails.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"217 ","pages":"Article 110290"},"PeriodicalIF":0.9,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572986","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
Frank copula is minimum information copula under fixed Kendall’s τ 在固定的 Kendall's τ 条件下，弗兰克协程是最小信息协程。
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-10-26 DOI: 10.1016/j.spl.2024.110289
Issey Sukeda , Tomonari Sei
{"title":"Frank copula is minimum information copula under fixed Kendall’s τ","authors":"Issey Sukeda ,&nbsp;Tomonari Sei","doi":"10.1016/j.spl.2024.110289","DOIUrl":"10.1016/j.spl.2024.110289","url":null,"abstract":"<div><div>In this work, we demonstrate that the Frank copula is the minimum information copula under fixed Kendall’s <span><math><mi>τ</mi></math></span> (MICK), both theoretically and numerically. First, we explain that both MICK and the Frank density follow the hyperbolic Liouville equation. Subsequently, we show that the copula density satisfying the Liouville equation is uniquely the Frank copula. Our result asserts that selecting the Frank copula as an appropriate copula model is equivalent to using Kendall’s <span><math><mi>τ</mi></math></span> as the sole available information about the true distribution, based on the entropy maximization principle.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"217 ","pages":"Article 110289"},"PeriodicalIF":0.9,"publicationDate":"2024-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142551915","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
Minimizing the penalized goal-reaching probability with multiple dependent risks 最小化多重依赖风险下的惩罚性目标达成概率
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-10-24 DOI: 10.1016/j.spl.2024.110287
Ying Huang, Jun Peng
{"title":"Minimizing the penalized goal-reaching probability with multiple dependent risks","authors":"Ying Huang,&nbsp;Jun Peng","doi":"10.1016/j.spl.2024.110287","DOIUrl":"10.1016/j.spl.2024.110287","url":null,"abstract":"<div><div>We consider a robust optimal investment and reinsurance problem with multiple dependent risks for an Ambiguity-Averse Insurer (AAI), who wishes to minimize the probability that the value of the wealth process reaches a low barrier before a high goal. We assume that the insurer can purchase per-loss reinsurance for every class of insurance business and invest its surplus in a risk-free asset and a risky asset. Using the technique of stochastic control theory and solving the associated Hamilton-Jacobi-Bellman (HJB) equation, we derive the robust optimal investment-reinsurance strategy and the associated value function. We conclude that the robust optimal investment-reinsurance strategy coincides with the one without model ambiguity, but the value function differs. We also illustrate our results by numerical examples.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"217 ","pages":"Article 110287"},"PeriodicalIF":0.9,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572987","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
Pricing formula of Lookback option in stochastic delay differential equation model 随机延迟微分方程模型中的回溯期权定价公式
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-10-17 DOI: 10.1016/j.spl.2024.110283
Paek Il-Kwang , Kang Chol-Su , Kim Kyong-Hui
{"title":"Pricing formula of Lookback option in stochastic delay differential equation model","authors":"Paek Il-Kwang ,&nbsp;Kang Chol-Su ,&nbsp;Kim Kyong-Hui","doi":"10.1016/j.spl.2024.110283","DOIUrl":"10.1016/j.spl.2024.110283","url":null,"abstract":"<div><div>This paper deals with new explicit pricing formulae for Lookback option when underlying asset price processes are represented by stochastic delay differential equation (hereafter “SDDE”). We derive a lemma on the joint distribution of the minimum and itself of a Wiener process in the SDDE model. Using this lemma, we obtain the explicit pricing formulae for the Lookback option. Through some numerical comparison experiment, we assure the correctness of the obtained pricing formula.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"216 ","pages":"Article 110283"},"PeriodicalIF":0.9,"publicationDate":"2024-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142527950","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
Well-posedness for the stochastic Landau–Lifshitz–Gilbert equation with helicity driven by jump noise 具有跳变噪声驱动的螺旋的随机朗道-利夫希茨-吉尔伯特方程的良好拟合
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-10-15 DOI: 10.1016/j.spl.2024.110285
Soham Gokhale
{"title":"Well-posedness for the stochastic Landau–Lifshitz–Gilbert equation with helicity driven by jump noise","authors":"Soham Gokhale","doi":"10.1016/j.spl.2024.110285","DOIUrl":"10.1016/j.spl.2024.110285","url":null,"abstract":"<div><div>We consider the stochastic Landau–Lifshitz–Gilbert equation driven by pure jump noise. We assume non-zero contribution from the helicity term to the total energy. Using finite dimensional approximation followed by a generalization of the Jakubowski’s version of the Skorohod Theorem for non-metric spaces, we show that the considered problem admits a weak martingale solution. Restricting the problem to dimension 1, we show that the obtained solution is pathwise unique, thereby concluding the existence of a strong solution.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"216 ","pages":"Article 110285"},"PeriodicalIF":0.9,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142527949","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
Optimal curing rate allocation in the SIS epidemic model SIS 流行病模型中的最佳固化率分配
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-10-15 DOI: 10.1016/j.spl.2024.110284
Ryan McFadden, Fraser Daly, Seva Shneer
{"title":"Optimal curing rate allocation in the SIS epidemic model","authors":"Ryan McFadden,&nbsp;Fraser Daly,&nbsp;Seva Shneer","doi":"10.1016/j.spl.2024.110284","DOIUrl":"10.1016/j.spl.2024.110284","url":null,"abstract":"<div><div>We consider a susceptible-infected-susceptible (SIS) epidemic model on an undirected graph, with a homogeneous infection rate and heterogeneous curing rates. We set an overall network curing rate, <span><math><mi>Δ</mi></math></span>, and study optimal allocation of curing rates to nodes, in terms of the expected time to the extinction of the epidemic. As other parameters are fixed, we study these allocations as the infection rate tends to 0 and <span><math><mi>∞</mi></math></span> in both regular and non-regular graphs. We further illustrate this optimisation with some numerical examples. Our findings demonstrate that, while the uniform split of <span><math><mi>Δ</mi></math></span> is optimal in some situations, it is typically not optimal, even for regular graphs.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"216 ","pages":"Article 110284"},"PeriodicalIF":0.9,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142527951","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
Statistical inference for Ornstein–Uhlenbeck processes based on low-frequency observations 基于低频观测的 Ornstein-Uhlenbeck 过程的统计推断
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2024-10-15 DOI: 10.1016/j.spl.2024.110286
Dingwen Zhang
{"title":"Statistical inference for Ornstein–Uhlenbeck processes based on low-frequency observations","authors":"Dingwen Zhang","doi":"10.1016/j.spl.2024.110286","DOIUrl":"10.1016/j.spl.2024.110286","url":null,"abstract":"<div><div>Low-frequency observations are a common occurrence in real-world applications, making statistical inference for stochastic processes driven by stochastic differential equations (SDEs) based on such observations an important issue. In this paper, we investigate the statistical inference for the Ornstein–Uhlenbeck (OU) process using low-frequency observations. We propose modified least squares estimators (MLSEs) for the drift parameters and a modified quadratic variation estimator for the diffusion parameter based on the solution of the OU process. The MLSEs are derived heuristically using the nonlinear least squares method, despite the OU process satisfying a linear SDE. Unlike previous approaches, these modified estimators are asymptotically unbiased. Leveraging the ergodic properties of the OU process, we also propose ergodic estimators for the three parameters. The asymptotic behavior of these estimators is established using the ergodic properties and central limit theorem for the OU process, achieved through linear model techniques and multivariate Markov chain central limit theorem. Monte Carlo simulation results are presented to illustrate and support our theoretical findings.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"216 ","pages":"Article 110286"},"PeriodicalIF":0.9,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142527948","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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