非线性模型中M-估计的Bootstrap逼近

讨论了非线性模型中回归系数向量基于M-估计的Bootstrap逼近,并在一定的条件下证明了Bootstrap逼近成立。     

删失数据下一类回归模型的参数估计

考虑一类回归模型,在右删失数据下构造了参数的最小二乘估计和加权最小二乘估计,证明了估计量具有渐近正态性。模拟结果表明加权最小二乘估计比最小二乘估计有优良的性质。     

多维门限自回归模型参数估计的渐近正态性

对多维门限自回归模型的参数估计,宋心远等在1990年给出了自回归系数矩阵最小二乘估计的强相容性,由此进一步得到了此估计的渐近正态性。     

基于Bootstrap方法的过程能力指数区间估计

针对传统统计过程控制方法的局限性,利用Bootstrap方法构建了过程能力指数的置信区间,分别对正态分布、指数分布进行仿真计算,对3种Bootstrap置信区间进行了比较。通过实证分析验证了在小样本条件下Bootstrap置信区间的有效性。     

半变系数模型约束PLS估计的渐近正态性

半变系数模型已经获得了广泛的研究和应用,近几年,人们提出许多方法来估计其函数系数和常系数.在PLS方法基础上,本文给出半变系数模型模型在线性随机约束条件下的估计,并证明了常系数和函数系数估计的渐近正态性.     

密度函数递归核估计的Bootstrap逼近

设X1，X2，…xn是从分布密度函数为f（x）的总体中抽取的独立同分布的样本，f（x）的递归核估计fn（x），本文讨论了fn（x）的渐近正态性以及Bootstrap逼近问题．     

部分线性模型中参数分量与非参数分量估计的收敛速度

对于部分线性回归模型,基于未知函数 ｆ （·） 与 ｇ （·） 分别取一类核估计和最近邻估计,文中构造了参数β的最小二乘估计β和加权最小二乘估计β,获得了参数β估计量的渐近正态性与函数ｇ （·） 估计量的最优弱收敛速度。     

风险度量ES的非参数估计

期望损失(Expected Shortfall,ES)是当今最流行的金融资产风险度量的工具之一,是一个理想的一致性风险度量.本文在α-混合序列具有幂衰减混合系数的条件下,讨论了风险度量ES的样本估计量的性质,得到估计量的Bahadur表示以及渐近正态性.     

NA样本下固定设计回归估计的渐进正态性

对于固定设计回归模型，本文在NA样本、强平稳及较弱的条件下建立了回归权函数估计的渐近正态性，应用这一结果具体地讨论了Gasser-Muller估计和Priesfley-Chao估计，得到相应的结论。     

m相依样本均值随机加权估计的渐近性质

本文利用基于刀切虚拟值的随机加权法，解决了ｍ相依样本均值随机加权逼近的相合性问题。     

《指数摩擦力模型振动系统的动态特性研究》

研究了单自由度滑动摩擦系数随相对速度指数变化的干摩擦振动系统简谐激励响应计算问题,应用等效线性化方法推导了相应的频响方程。通过数值分析,明确了各个系统参数对干摩擦系统振动的影响。     

Estimation of the Parameters of a Mixture of Exponential and Weibull Distributions with Progressive Censoring

A method is proposed for estimating the parameters of a mixture of exponential and Weibull distributions using censored samples. Preliminary estimates obtained by graphical analysis are refined by the method of maximum likelihood. The efficiency of the method is confirmed by the results of a statistical modeling.     

一类具有Markovian参数的随机微分时滞方程的指数稳定性

对Hilbert空间中具有Markovian参数的随机泛函微分时滞方程的指数稳定性进行了讨论。利用指数鞅公式,Lyapunov函数和一些不等式给出系统指数稳定的充分条件。这是对已有结果的完善和推广。通过一个例了对本文的结论进行了说明。     

改进的特征值修正方法及其在阻尼结构复模态综合中的应用

本文在特征值修正方法的基础上提出了一种阻尼结构的复模态综合方法。该方法特别适合于部件对接界面自由度较少情况下的阻尼结构模态综合。文章对复模态综合中子结构具有刚体位移情况提出了具体的处理方法,推导了一种考虑刚体位移的特征值修正方法方式。同时,为了在模态截尾情况下提高综合精度,在特征值修正方法中计入了剩余柔度的影响,推导了综合过程中剩余柔度的递推计算公式。给出了一个算例说明方法的有效性。     

刻度指数族参数的经验Bayes估计收敛速度的改进

本文对刻度指数族在加权平方损失下获得了参数的Bayes估计,利用基于Bessel函数的核估计方法构造了相应的经验Bayes(EB)估计,证明了所提出的EB估计具有收敛速度O((n-1In10)λδ-2 δ),此处δ≥2,1/2<λ<1.最后,给出了一个例子,说明适合定理条件的先验分布是存在的.     

测量过程控制图参数的自助最大熵融合优化

Shewhart控制图是核查数据分析的主要工具,在核查数据为小样本情况下Shewhart控制图容易导致“误发警报”。针对这一问题,提出一种自助最大熵融合方法,优化Shewhart控制图控制参数。首先,通过自助法充分挖掘核查数据自身特征,扩大样本容量。在此基础上,应用最大熵原理,描述出核查数据概率分布参数的密度函数,估计核查数据样本的均值和方差,从而优化Shewhart控制图控制参数。实验表明,经自助最大熵优化后的Shewhart控制图控制参数更加接近理论值,降低了发生“误发警报”的概率。     

渐近信号瞬态频率的提取

由渐近信号的小波分析出发，研究了渐近信号小波变换的渐近估计方法。着重讨论了渐近信号在小波变换下的特征，构造了信号瞬态频率提取的实现算法。最后结合仿真数值，得到了较好的结果。     

On the Stability of Exponential Backoff

Random access schemes for packet networks featuring distributed control require algorithms and protocols for resolving packet collisions that occur as the uncoordinated terminals contend for the channel. A widely used collision resolution protocol is the exponential backoff (EB). New analytical results for the stability of the (binary) EB are given. Previous studies on the stability of the (binary) EB have produced contradictory results instead of a consensus: some proved instability, others showed stability under certain conditions. In these studies, simplified and/or modified models of the backoff algorithm were used. In this paper, care is taken to use a model that reflects the actual behavior of backoff algorithms. We show that EB is stable under a throughput definition of stability; the throughput of the network converges to a non-zero constant as the offered load N goes to infinity. We also obtain the analytical expressions for the saturation throughput for a given number of nodes, N. The analysis considers the general case of EB with backoff factor r, where BEB is the special case with r = 2. We show that r = 1/(1 − e⁻¹) is the optimum backoff factor that maximizes the throughput. The accuracy of the analysis is checked against simulation results.     

Exponential basis functions in solution of static and time harmonic elastic problems in a meshless style

In this paper, exponential basis functions (EBFs) are used in a boundary collocation style to solve engineering problems whose governing partial differential equations (PDEs) are of constant coefficient type. Complex‐valued exponents are considered for the EBFs. Two‐dimensional elasto‐static and time harmonic elasto‐dynamic problems are chosen in this paper. The solution procedure begins with first finding a set of appropriate EBFs and then considering the solution as a summation of such EBFs with unknown coefficients. The unknown coefficients are determined by the satisfaction of the boundary conditions through a collocation method with the aid of a consistent and complex discrete transformation technique. The basis and various forms of the transformation have been addressed and discussed. We shall propose several strategies for selection of EBFs with the aid of the basis explained for the transformation. While using the transformation, the number of EBFs should not necessarily be equal to (or less than) the number of boundary information data. A library of EBFs has also been presented for further use. The effect of body forces is included in the solution via construction of particular solution by the use of the discrete transformation and another series of EBFs. A number of sample problems are solved to demonstrate the capabilities of the method. It has been shown that the time harmonic problems with high wave number can be solved without much effort. The method, categorized in meshless methods, can be applied to many other problems in engineering mechanics and general physics since EBFs can easily be found for almost all problems with constant coefficient PDEs. Copyright © 2009 John Wiley & Sons, Ltd.