On Nonsmooth Estimating Functions via Jackknife Empirical Likelihood

In many applications, the parameters of interest are estimated by solving non‐smooth estimating functions with U‐statistic structure. Because the asymptotic covariances matrix of the estimator generally involves the underlying density function, resampling methods are often used to bypass the difficulty of non‐parametric density estimation. Despite its simplicity, the resultant‐covariance matrix estimator depends on the nature of resampling, and the method can be time‐consuming when the number of replications is large. Furthermore, the inferences are based on the normal approximation that may not be accurate for practical sample sizes. In this paper, we propose a jackknife empirical likelihood‐based inferential procedure for non‐smooth estimating functions. Standard chi‐square distributions are used to calculate the p‐value and to construct confidence intervals. Extensive simulation studies and two real examples are provided to illustrate its practical utilities.     

随机扰动下激励系统的分岔与控制研究

为研究激励系统分岔现象的控制问题,首先基于系统理论,分析激励系统的整体涌现性、非线性、鲁棒性和稳定性问题,运用随机非线形理论中的随机平均法和随机过程理论研究了激励系统的随机扰动和分岔问题,提出参数临界状态下,激励系统分岔平衡点稳定性方程,并进一步给出系统存在跨临界分岔和奇异诱导分岔的充分条件。最后,设计反馈控制器,通过控制能量和调整平衡点,抑制激励分岔,使系统趋于稳定。     

An analytical approximation method for pricing barrier options under the double Heston model

Abstract

The purpose of the paper is to provide an efficient pricing method for single barrier options under the double Heston model. By rewriting the model as a singular and regular perturbed BS model, the double Heston model can separately mimic a fast time-scale and a slow time-scale. With the singular and regular perturbation techniques, we analytically derive the first-order asymptotic expansion of the solution to a barrier option pricing partial differential equation. The convergence and efficiency of the approximate method is verified by Monte Carlo simulation. Numerical results show that the presented asymptotic pricing method is fast and accurate.     

广义Cholesky分解新的扰动分析

设实对称矩阵K具有广义Cholesky分解,证得扰动矩阵的广义Cholesky分解满足：｜｜ΔL｜｜F/｜｜L｜｜2≤Kc（k）ε＋O（ε^2）．例子表明此扰动结果比以往的结果更精确．     

Computing AIC for black-box models using generalized degrees of freedom: A comparison with cross-validation

Generalized degrees of freedom (GDF), as defined by Ye (1998 Ye, J. (1998). On measuring and correcting the effects of data mining and model selection. Journal of the American Statistical Association 93(441):120–131. [Google Scholar] JASA 93:120–131), represent the sensitivity of model fits to perturbations of the data. Such GDF can be computed for any statistical model, making it possible, in principle, to derive the effective number of parameters in machine-learning approaches and thus compute information-theoretical measures of fit. We compare GDF with cross-validation and find that the latter provides a less computer-intensive and more robust alternative. For Bernoulli-distributed data, GDF estimates were unstable and inconsistently sensitive to the number of data points perturbed simultaneously. Cross-validation, in contrast, performs well also for binary data, and for very different machine-learning approaches.     

带有多面体扰动的半监督v-支持向量分类机

在通常建立的优化模型中,一般都假定输入的数据是精确的,而实际生活中我们得到的数据总会带有测量或统计误差,因此,本文考虑数据在多面体内扰动的半监督两类问题,以v-支持向量分类机为基础,借鉴把半监督两类分类问题转化为一个凹规划的思想,给出数据在多面体内扰动的半监督v-支持向量分类算法。该算法的参数v易于选择,而数值试验也表明该算法具有良好的稳定性和较好的分类结果。     

不均匀媒质填充矩形弯曲波导的研究(英文)

在圆柱坐标系中对径向不均匀媒质填充的矩形弯曲波导进行了研究。在截止频率上,波导中的电磁场可分解为E模和H模。利用摄动理论和低阶模近似,讨论了特征方程。研究表明,HE模和EH模在弱不均匀媒质和低阶模近似条件下是简并的。     

策略集扰动下Nash平衡的精炼

通过定义一种策略集的扰动映射,引入一种新的稳定Nash平衡的概念,并利用Ky Fan不等式定理的相关结果证明该稳定Nash平衡的存在性.     

Local influence regression diagnostics for gamma data

The local influence diagnostics proposed in general terms irl Cook (1986), Thomas and Cook (1989) and Billor and Loynes (1993). arc adapted for gamma data. A data set prcviously analysed using different methods is then reexamined, and conclusions based on wing the new approach are made.     

间隙非线性齿轮系统混沌运动的自适应脉冲控制

将自适应脉冲控制法应用到一类单级间隙非线性齿轮系统,在控制参量中加入自适应控制方法,通过调节自适应控制器产生的脉冲强度将系统的混沌运动镇定到不同的周期轨道。数值模拟结果表明了该方法的有效性和较强的鲁棒性。