In this paper,we consider the limiting distribution of the maximum interpoint Euclidean distance Mn=max1≤i＜j≤n ∥Xi-Xj∥,where X1,X2,…,Xn be a random sample drawn from a p-dimensional population with dependent sub-Gaussian components.When the dimension tends to infinity with the sample size,we prove that M2n under a suitable normalization asymptotically obeys a Gumbel-type distribution.The proofs mainly rely on the Chen-Stein Poisson approximation method and high-dimensional Gaussian approximation.
We study a finite number of independent random walks with subexponentially dis-tributed increments and negative drifts.We extend the one-dimensional results to finite and fully general stopping times.Assuming that the distribution of the lengths of these intervals is relatively light compared to the distribution of the increments of the random walks,we derive the asymptotic tail distribution of the partial maximum sum over the random time interval.
We investigate the complete p th moment convergence for weighted sums of independent, identically distributed random variables under sublinear expectations space. Using moment inequality and truncation methods, we prove the equivalent conditions of complete p th moment convergence of weighted sums of independent, identically distributed random variables under sublinear expectations space, which complement the corresponding results obtained in Guo and Shan (2020).
Industrial systems often have redundant structures for improving reliability and avoiding sudden failures, and a parallel system is one of the special redundant systems. In this paper, we consider the problem of reliability estimation for a parallel system when one stress variable is involved, which is called the multicomponent stress-strength model. The parallel system contains two components, and their joint lifetime follows a Marshall–Olkin bivariate Weibull distribution, while the stress variable is assumed to be the Weibull distribution. Due to the complicated form of the likelihood function, a data augmentation method is proposed, and then the Gibbs sampling algorithm is constructed to obtain the Bayesian estimation of the system reliability. The proposed method is evaluated by a simulated dataset and Monte Carlo simulation study. The simulation results show that the proposed method performs well in terms of relative bias, mean squared error and frequentist coverage probability.
本文考虑一类带有移民和瞬态拯救的二次加权分枝过程.在拯救速率可和的条件下,证明了目标过程不存在.研究拯救速率不可和的情形,得到了过程存在性判别准则与唯一性判别准则,并针对存在性给出了便于验证的等价条件.对于满足存在性条件的q矩阵Q,证明可以找出无穷多个Q过程,其中不中断Q过程却是唯一的.讨论了不中断Q过程的构造方式,证明了不中断Q过程是遍历的,且给出了平稳分布满足的二阶微分方程.
Semi-supervised data contains a labeled data set with both responses and covariates and an unlabeled data set with covariates only.The inference based on semi-supervised data is gaining more and more interests in statistics.When the response in the labeled data is binary,case-control sampling is commonly used to alleviate the imbalanced data structure.When the response and the covariates satisfy the logistic model,the slope parameter of the model can be consistently estimated even for the case-control sampling.However,when the logistic model is incorrectly specified for the data,the case-control samples can not estimate the population risk minimizer consistently.With the help of the unlabeled data,we derive a consistent estimator for the case population proportion.Then,an inverse probability weighted loss function is developed to obtain a consistent estimator for the population risk minimizer.The proposed estimators are shown to be asymptotically normal and the limiting variance-covariance matrix can be consistently estimated.Simulation results show that the proposed method gives out reasonable finite sample performances.A real data example is also analyzed for illustration.
本文研究了连续时间考虑相对收益的两个风险厌恶机构投资者之间的最优投资选择博弈问题.假设机构投资者可以投资于相同的无风险资产和不同的具有相关关系的风险股票,以反映投资的资产专门化.机构投资者选择动态投资策略使得期望终端绝对收益和相对收益权重和的效用最大.首先,我们定义了 Nash均衡投资策略.其次,在机构投资者具有指数效用函数下,得到了 Nash均衡投资策略和值函数的显示表达式,分析了相对收益对Nash均衡投资策略和值函数的影响,并通过数值计算给出了 Nash均衡投资策略与模型主要参数之间的关系.最后,采用确定性等价比较了考虑相对收益的最优投资策略与仅仅考虑绝对收益的最优投资策略的投资绩效,结果表明相对收益会影响机构投资者的投资绩效.
本文考虑对具有扩散扰动影响的复合泊松风险模型下的破产概率进行非参数估计.我们基于复傅里叶级数展开方法(CFS)对破产概率进行逼近,并利用索赔次数和索赔额的随机样本值对破产概率进行非参数估计.同时我们还对估计量在大样本下进行了误差分析,提供了模拟结果,验证了在样本量有限下这种估计方法的有效性.
概率组合方法是分析无线传感器网络(wireless sensor network,WSN)可靠性的重要方法,它能够有效处理该网络中的隔离效应和竞争失效问题.然而,已有文献中基于概率组合方法的WSN可靠性建模和计算存在一些缺陷,导致研究结果应用范围受限甚至错误地评估WSN的可靠性.本文研究了一类典型的WSN——具有随机依赖机制的单中继器WSN的可靠性建模与计算.在组件局部失效和外部攻击导致全局失效的竞争失效机制下,建立了 WSN更符合实际亦更严谨的可靠性模型,基于严格的概率组合分析,呈现了系统化的可靠性计算方法和计算公式,改进了文献中关于此类问题的研究.最后,作为算法应用展示,我们计算了两个特殊的WSN——身体传感网络和空气监测系统的可靠性.
Consider a nearest-neighbor random walk with certain asymptotically zero drift on the positive half line.Let M be the maximum of an excursion starting from 1 and ending at 0.We study the distribution of M and characterize its asymptotics,which is quite different from those of simple random walks.
精准医疗强调了正确识别异质性子群的重要性,以发展可针对每个子群的个性化治疗方案.尽管近来在子群分析的方法上取得了一些进展,在数据存在删失时,如何有效识别子群仍然缺乏探索.在本文中,我们提出了一种基于加速失效模型的新的子群分析方法,其中由潜在因素导致的异质性可以用特定于个体的截距项来表示.我们考虑最常见的右删失情况,并利用平均插补法对删失数据进行处理.硬阈值惩罚函数被应用于配对截距项的成对差值,可以自动地将观察个体划分为不同的子群.我们也建立了所提出的估计量的理论性质.模拟研究和威斯康辛乳腺癌数据集分析进一步验证了所提方法的有效性.
对常利率下保费收入为复合Poisson过程风险模型的分红问题进行研究,得到了直至破产时累积分红现值的期望、n阶矩及矩母函数满足的积分 微分方程及指数保费和指数索赔下的具体表达式.并给出数值算例,分析了初始资本u、红利界限6及投资利率r对累积分红期望现值的影响.
Currently,spectroscopy technology is widely used in traditional Chinese medicine analysis.In this paper,from the functional data analysis perspective,we study outlier detection methods for spectral data,detect outliers,and propose the"Oja depth detection method".Sim-ulation studies demonstrate the advantages of the Oja depth detection method.We compare the Oja depth detection method with three existing methods on a Chinese medicine spectral data of 73-dose six-mixture liquid.The results show the proposed Oja depth method is able to detect all six unqualified samples and has the highest accuracy.
成分正交表是适用于添加顺序实验的一种有效的设计方法.本文利用首列相同的正交拉丁方构造出了因子个数为素数幂时的成分正交表,并在此基础上构造出了因子数可取任意正整数的成分正交表.所得设计的一些优良投影性质也得到了证明.
设{X,Xn,n≥1}是同分布的NA随机变量序列,h(·)＞0是定义在(0,∞)上的不减函数且满足∫1∞[th(t)]-1d t=∞.令ψ(t)=.∫t1[sh(s)]-1ds,t≥1,Sn=∑ni=1Xi,n≥1,Lt=lnmax{e,t}.本文证明了 ∑∞n=1[nh(n)]-1P(max1≤j≤n|Sj|≥(1+ε)σ√2nLψ(n))＜∞,∀ε＞0 成立的充要条件是E(X)=0和E(X2)=σ2 ∈(0,∞).这一结果部分地推广了文献[7]的结论.
一、《应用概率统计》是中国数学会概率统计学会主办的全国性学术刊物,刊登概率论与数理统计领域在理论或应用方面具有创新的学术论文,包括最新成果的综述报告,并选登高等学校和科研单位的教学与应用成果简报. 二、来稿要求和注意事项: 1.来稿请采用Ctex或LaTeX按本刊模板排版,自留底稿.来稿需控制在15页以内,可在投稿时增加附录.原稿必须是在中外文正式刊物上未发表的论文.本刊严禁一稿多投,重复内容多次投稿.一年后本刊尚未处理结束的来稿,作者如需改投它刊,务必来函通知本刊编辑部.
This paper considers a risk probability minimization problem for nonstationary discrete-time Markov decision processes,in which the transition probabilities and the reward func-tions depend on time.Different from the expected reward/cost criteria in the existing literature,the optimality performance here is to minimize the probability that the total rewards do not reach a given profit goal until the first passage time to some target set.Under mild reasonable conditions,we establish the corresponding optimality equations,verify that the sequence of the optimal risk functions is the unique solution to the optimality equations,and prove the existence of an optimal Markov policy.
本文研究在随机工资和模型不确定性影响下确定缴费型养老金的鲁棒最优投资问题.在模型中,养老金账户中的资本可以投资于一种风险资产和一种无风险资产,假设风险资产价格满足Heston模型.研究目标是通过选择最优投资策略,使得养老金账户的终端相对财富效用最大化.利用随机动态规划的方法,我们求出了在幂效用函数和指数效用函数下鲁棒最优投资策略和相应的值函数.最后,通过MATLAB软件对理论结果进行了数值分析.
本文考虑半马氏决策过程的指数效用最优问题,其中状态和行动空间均为Borel集,报酬函数非负.最优准则是最大化系统无限阶段内获取总报酬指数效用的期望值.首先,建立标准正则性条件确保状态过程非爆炸,连续紧条件确保最优策略存在.其次,基于这些条件,利用值迭代和嵌入链技术,证明了值函数是相应最优方程的唯一解以及最优策略的存在性.最后,通过实例展示了如何利用值迭代算法计算值函数和最优策略.
对于高维空间回归问题,本文提出了一种有效的稀疏贝叶斯模型.通过引入分层高斯马尔可夫随机场先验,模型可以获取稀疏的空间变化参数,同时对于相邻的空间区域也可以获取同质的参数.相较于传统的采样方法,本文采用一种快速收敛的变分EM算法进行后验推断.对于M步,最优化问题可以通过简单的变形转化为经典的自适应lasso问题进行快速求解.通过数值模拟可以发现模型在参数估计和变量选择问题上取得较好的效果.最后模型用来分析欧洲社会人口学因素对各国新冠死亡率的影响.
