平稳遍历马氏链部分和序列最小值分布的渐近估计及其应用

本文给出了有限状态平稳遍历Markov链部分和序列最小值分布的一个渐近估计式并利用它对一类Athreya-KarlinBPRE．灭种概率的渐近行为作出估计．     

考虑Markov保费和利率的离散时间风险模型的破产概率

研究一类离散时间风险模型的破产概率.在保费收入和利率同时为离散时间Markov链,索赔额为独立情形下,利用更新迭代方法得到最终时间破产概率的Lundberg型上界.     

形状约束条件下Bayes非参数回归

本文给出形状约束条件下非参数回归模型的Bayes估计方法.利用Markov链Monte Carlo方法对模型进行拟合.具体地,用形状约束Bernstein多项式近似非参数函数,把截断正态分布作为Bernstein多项式系数的先验分布来保证函数估计满足指定的形状约束.最后通过模拟比较和实例分析来展现形状约束Bayes估计的小样本性质.     

微分算子和边界双摄动的高阶椭圆型方程的狄立克雷问题

本文研究了在边界和算子摄动相结合的情况下高阶椭圆型方程解的渐近式的构造.如果非摄动问题A₀不在谱上,则摄动问题A_ε的渐近解可按小参数ε的次幂展开;如果A₀在谱上,则在A_ε的渐近解中出现有小参数ε的负幂;同时给出了有关的余项的估计.     

中国产业结构转移的Markov链

本文提出了系统的结构圆概念 ,引入了结构圆上的 Markov链 ,并且将这一模型应用于我国产业结构转移运动的模拟与研究 .文中完成了产业结构转移概率的估计 ,并且根据估计结果 ,对我国不同时期产业结构的转移运动进行了比较分析     

通过消息监控识别罪犯的Markov模型

通过消息监控识别罪犯是一个十分有意义的实际问题。本文采用Markov模型的方法,将整个消息传递网络看作一个犯罪传递的Markov链.根据所收集到的消息估计出两个节点（人）之间犯罪传递的概率,得到一个Markov概率转移矩阵,并求出网络长期运行下去的稳定解,作为各节点（人）参与犯罪程度的度量。文章通过实例说明该方法的有效性。     

带有Markov型误差的线性模型的假设检验（英文）

本文研究线性模型中关于误差Markov链齐次性的假设检验问题.利用关于未知参数的拟极大似然估计和鞅差方法,获得了似然比检验统计量的极限分布.     

门限自回归模型参数估计的渐近性质

本文在给定门限自回归模型阶数、门限及延迟参数的情况下,通过研究模型所构成Markov链的一些性质,得到了自回归系数最小二乘法估计的强相容性与渐近正态性。同时,还证明了白噪声方差的估计亦具有强相容性。     

客户回报随机过程的Markov性和时间齐次性

在客户发展关系的Markov链模型的基础上,构建了企业的客户回报随机过程．证明了：在适当假设下,客户回报过程是Markov链。甚至是时间齐次的Markov链．本文求出了该链的转移概率．通过转移概率得到了客户给企业期望回报的一些计算公式,从而为企业选定发展客户关系策略提供了有效的量化基础．     

连续时间Markov链的遍历度

以首中时的矩来研究连续时间Markov链高阶偏差矩阵的存在及有限性, 并由此给出转移矩阵收敛到平稳分布的多项式速度的估计. 对于生灭过程, 给出了显式的表达式.     

故障概率模型的建立与估算定理的推证

基于网络部件故障概率及其更新的随机过程,应用RRM和CTMC分析马尔科夫概率模型MPM的建立,讨论在基本条件下的故障概率重要定理和可靠性概率估计的应用公式.     

Analysis of Numerical Differentiation Formulas in a Boundary Layer on a Shishkin Grid

A problem of numerical differentiation of functions with large gradients in a boundary layer is investigated. The problem is that for functions with large gradients and a uniform grid the relative error of the classical difference formulas for derivatives may be considerable. It is proposed to use a Shishkin grid to obtain a relative error of the formulas that is independent of a small parameter. Error estimates that depend on the number of nodes of the difference formulas for a derivative of a given order are obtained. It is proved that the error estimate is uniform with respect to the small parameter. In the case of a uniform grid, a boundary layer region is indicated outside of which the numerical differentiation formulas have an error that is uniform with respect to the small parameter. The results of numerical experiments are presented.     

恒应力寿命试验截尾模型参数的最佳估计

对恒定应力加速寿命试验建立了定时截尾与定数截尾参数模型.在诂计模型参数时,考虑定时截尾产品失效数的随机性,引入近似因子、修偏乘子和修偏项,建立起参数估计通用式并逐次进行跟随修偏估计.对定数截尾考虑数据信息随机性短缺,通过变量变换分别建立最优线性无偏估计和简单线性无偏估计在指数分布条件下的式子,并按统计分析考虑随机因数的影响引入综合修偏因子,按抽样数目的多少分别采用修偏后的式子.最后应用实际数据对模型参数逐次修偏估计和不同估计方法对比的最佳估计.     

The error and guaranteed accuracy of cubature formulas in multidimensional periodic Sobolev spaces

We give an upper bound for the deviation of the norm of a perturbed error from the norm of the original error of a cubature formula in a multidimensional bounded domain. The deviation arises as a result of the joint influence on the computations of small variations of the weights of a cubature formula and rounding in the subsequent calculations of the cubature sum in the given standards (formats) of approximation to real numbers. We estimate the practical error of a cubature formula acting on an arbitrary function from the unit ball of a normed space of integrands. The resulting estimates are applied to studying the practical error of cubature formulas in the case of integrands in Sobolev spaces on a multidimensional cube. The norm of the error in the dual space of the Sobolev class is represented as a positive definite quadratic form in the weights of the cubature formula. We estimate the practical error for cubature formulas constructed as the direct product of quadrature formulas of rectangles along the edges of the unit cube. The weights of this direct product are positive.     

带插值条件的拟线性最小二乘估计

提出了带插值点的拟线性最小二乘法,并给出了带插值点的拟线性最小二乘法拟合的最小二乘估计,证明了及其参数具有无偏性。     

Errors, condition numbers, and guaranteed accuracy of higher-dimensional spherical cubatures

We give upper bounds for the deviation of the norm of a perturbed error functional from the norm of the original error of a higher-dimensional spherical cubature formula. The deviation arises as a result of the combined influence on the computation of small variations of the weights of the cubature formula and rounding for the subsequent calculation of the cubature sum in the given standards of approximation to real numbers. We estimate the practical error of the cubature formula for its action on an arbitrary function in the unit ball of the normed space of integrands. The resulting estimates are applied to studying the practical error of spherical cubature formulas in the case of integrands in Sobolev-type spaces on the higher-dimensional unit sphere. We represent the norm of the error functional in the dual space of the Sobolev class as a positive definite quadratic form in the weights of the cubature formula. We estimate the practical error for spherical cubature formulas, each of which is constructed as the direct product of Gauss’s quadrature formula along the meridian of the sphere and of the rectangle quadrature formula along the equator. The weights of this direct product with 2m ² nodes are positive. The formula itself is exact at all spherical harmonics up to order 2m ? 1.     

增长曲线模型中回归系数的广义根方估计

本文对增长曲线模型中的回归系数B提出了一种新的估计形式－广义根方估计的B（K），其中K＝diag(k1,k2,…，kp）并证明了通过广义根方偏参数ki(i=1,2,…，p）的适当选取可使得该估计在均方误差矩阵的意义下优于已有的LS估计和根方估计，及广义根方估计是可容许估计，本文还给出了选取广义根方偏参数的两种方法，算法及一个应用实例。     

PARMA模型参数最小绝对偏差(LAD)估计量的极限分布

在最优化理论基础上,采用相对较稳健的最小绝对偏差（LAD）估计方法,首先研究了周期自回归滑动平均（PARMA）模型参数估计问题,得到了PARMA模型LAD估计量的渐近分布.其次对该模型的LAD估计作了进一步的讨论,给出更一般假设条件下模型参数LAD估计量的渐近性质。     

Relative Asymptotic Efficiency of the Maximum Pseudolikelihood Estimate for Gauss–Markov Random Fields

A general version of the maximum pseudolikelihood estimate of parameters within the class of Gauss–Markov random fields is stated in a rigorous way. Its asymptotic properties, namely the consistency, the asymptotic normality, and the relative asymptotic efficiency are studied. Explicit formulas for the asymptotic covariance matrix are given, and a decrease of efficiency is proved. A numerical example is added to show that the efficiency can be improved by enlarging the range of the conditional distribution used in the estimator. This revised version was published online in June 2006 with corrections to the Cover Date.     

基于偏差的不确定型多属性决策的综合集成方法

对不确定型条件下的多属性决策问题,规范化后的区间数能消除属性值之间量纲的差异,建立了相离度偏差、中间值偏差和理想方案偏差计算公式,构建了以总偏差平方和为目标函数的综合集成优化模型,求解出各属性的客观权重,提出了一种客观属性权重的可能度法,为不确定型多属性决策提供了一种简单实用的可靠方法.最后通过一个算例说明了该方法的实用性和有效性.