带随机效应非线性模型的影响分析

Abstract. In this paper,a unified diagnostic method for the nonlinear models with random ef-fects based upon the joint likelihood given by Robinson in 1991 is presented. It is shown that thecase deletion model is equivalent to the mean shift outlier model. From this point of view ,sever-al diagnostic measures, such as Cook distance, score statistics are derived. The local influencemeasure of Cook is also presented. A numerical example illustrates that the method is avail-able     

非线性测量误差模型的影响分析

本文对非线性测量误差模型给出了统一的诊断方法,并证明了数据删除模型与均值漂移模型的等价性,由此出发得到了Cook距离、残差、杠杆值等诊断统计量.本文还讨论了非线性测量误差模型的局部影响分析,并给出了一个具体应用实例.推广了Zhao & Lee(1995)的结果.     

Influence analysis on linear models with random effects

In this paper,a unified diagnostic method for linear models with random effects basedupon the joint likelihood given by Robinson gin 1991) is presented. The case deletion model is e-quivalent to mean shift outlier model,as well as case weights model. From this point of view,several new diagnostic measures,such as Cook disrance,WK diagnostics are derived. Some pre-vious results are improved. Numerical examples illustrate the method is available.     

具有高斯过程误差的函数型线性模型的统计诊断

提出了具有高斯过程误差的函数型回归模型的几种诊断方法.在此模型中,首先,在样条基的基础上,推导了回归系数函数的估计.随后,证明了数据删失模型和均值漂移模型的等价性.然后,研究了三种诊断方法,即残差分析、Cook距离和似然距离来诊断异常和强影响数据.最后,通过一个模拟例子和一个实例来阐述方法的有效性.     

On classifying inputs and outputs in DEA: A revised model

Cook and Zhu [Cook, W.D., Zhu, J., 2007. Classifying inputs and outputs in data envelopment analysis. European Journal of Operational Research 180, 692–699] introduced a new method to determine whether a measure is an input or an output. In practice, however, their method may produce incorrect efficiency scores due to a computational problem as result of introducing a large positive number to the model. This note introduces a revised model that does not need such a large positive number.     

偏正态数据下众数回归模型的统计诊断

为了更好地拟合偏态数据,充分提取偏态数据的信息,针对偏正态数据建立了众数回归模型,并基于Pena距离统计量对众数回归模型进行统计断研究,得到了众数回归模型的Pena距离表达式以及高杠杆异常点的诊断方法.利用EM算法与梯度下降法给出了众数回归模型参数的极大似然估计,根据数据删除模型计算似然距离、Cook距离和Pena距离统计量,绘制诊断统计图.通过Monte Carlo模拟试验和实例分析比较,说明文章提出的方法行之有效,并在一定条件下Pena距离对异常点或强影响点的诊断优于似然距离和Cook距离.     

具有AR(1)误差的非线性随机效应模型中自相关系数的扰动诊断

随机效应模型广泛应用于刻画重复测量数据的特征,Banerjee和Frees[1]用Cook距离,Lesaffre和Verbeke[2]用影响曲率分别对线性随机效应模型进行了分析.本文利用影响曲率对具有AR(1)误差的非线性随机效应模型中的自相关系数扰动进行了分析,得到了影响曲率的表达式,并且利用血浆药物渗透数据(Davidian和Gillinan[3])来说明分析方法的应用.     

Periodic solutions of certain hybrid delay-differential equations and their corresponding difference equations

In this paper we use a method due to Carvalho [L.A.V. Carvalho, On a method to investigate bifurcation of periodic solution in retarded differential equations, J. Difference Equ. Appl. 4 (1998) 17–27] to obtain conditions for the existence of nonconstant periodic solutions of certain systems of hybrid delay-differential equations. We first deal with a scalar equation of Lotka-Valterra type, followed by a system of 2 equations in 2 unknowns that could model the interactions of 2 identical neurons. It will be seen that such solutions are determined by solutions of corresponding difference equations. Another paper in which this method is used is by Cook and Ladeira [K.L. Cook, L.A.C. Laderia, Applying Carvalho’s method to find periodic solutions of difference equations, J. Difference Equ. Appl. 2 (1996) 105–115. [2]].     

Outlier Mining Based on Principal Component Estimation

Outlier mining is an important aspect in data mining and the outlier mining based on Cook distance is most commonly used. But we know that when the data have multicoUinearity, the traditional Cook method is no longer effective. Considering the excellence of the principal component estimation, we use it to substitute the least squares estimation, and then give the Cook distance measurement based on principal component estimation, which can be used in outlier mining. At the same time, we have done some research on related theories and application problems.     

MPM simulations of high-speed machining of Ti6Al4V titanium alloy considering dynamic recrystallization phenomenon and thermal conductivity

Ti6Al4V titanium alloy is often used in the aircraft industry due to its good strength and toughness etc. However, it is very difficult to simulate high speed machining of titanium alloy using the finite element method (FEM). The reason is that the high speed, large deformation and high strain rate of metal material at high temperature etc. will lead to the element distortions and other numerical difficulties. In contrast with FEM, material point method (MPM) has the advantage of simulating extreme large deformation, fracture and impact problems. Therefore, it is specially suitable for dealing with high speed cutting process. In many existing researches about the high speed cutting process using Johnson−Cook constitutive model, the material dynamic recrystallization softening effect under high pressure and high temperature has not been considered. For this, three modified Johnson−Cook constitutive models for Ti6Al4V titanium alloy are adopted and the parameters for these models were obtained by the split Hopkinson pressure bar (SHPB) test considering the critical strain values, high-temperature range and dynamic recrystallization phenomenon. Furthermore, to ensure the numerical accuracy, the transient heat conduction algorithm is employed in MPM implementation. Finally, comparison and discussion are carried out between the experimental and the simulation data, which show that the high speed cutting process can be better simulated using the modified Johnson−Cook constitutive models.     

基于Pena距离的加权最小二乘估计的影响分析

利用Pena距离对加权线性最小二乘估计的影响问题进行讨论,得到加权最小二乘估计的Pena距离的表达式,对其性质进行讨论,从而得到高杠异常点的判别方法.文中对Pena距离与Cook距离的性能进行了对比,得到在一定条件下Pena距离优于Cook距离的结论.并通过数值实验对此方法的有效性进行验证.     

Asymptotic solution of wave front of the telegraph model of dispersive variability

A number of nonlinear phenomena in physical, chemical, economical and biological processes are described by the interplay of reaction and diffusion or by the interaction between convection and diffusion. Recently, it is found that telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion for such branches of sciences. In this paper we use the technique of asymptotic solution to find travelling wave solution for the telegraph model of dispersive variability which is a generalization of the Julian Cook model. Our model tackled special values of the time delay and the probability that an individual is disperser in a population of dispersers and nondispersers. The solution of our model is reduced to telegraph Fisher–Kolmogoroff invasion and Julian Cook models. Also, the effect of the time delay on the propagation speed is presented.     

Asymptotic solution of wave front of the telegraph model of dispersive variability

A number of nonlinear phenomena in physical, chemical, economical and biological processes are described by the interplay of reaction and diffusion or by the interaction between convection and diffusion. Recently, it is found that telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion for such branches of sciences. In this paper we use the technique of asymptotic solution to find travelling wave solution for the telegraph model of dispersive variability which is a generalization of the Julian Cook model. Our model tackled special values of the time delay and the probability that an individual is disperser in a population of dispersers and nondispersers. The solution of our model is reduced to telegraph Fisher–Kolmogoroff invasion and Julian Cook models. Also, the effect of the time delay on the propagation speed is presented.     

Notes on classifying inputs and outputs in data envelopment analysis: A comment

Cook and Zhu (2007) introduced an innovative method to deal with flexible measures. Toloo (2009) found a computational problem in their approach and tackled this issue. Amirteimoori and Emrouznejad (2012) claimed that both Cook and Zhu (2007) and Toloo (2009) models overestimate the efficiency. In this response, we prove that their claim is incorrect and there is no overestimate in these approaches.     

具有一般协方差结构线性模型的局部影响评价

该文讨论了具有一般协方差结构线性模型的局部影响分析问题. 通过对广义Cook统计量中M/c的适当选取, 文章给出了一种对扰动的参数变换具有不变性质的局部影响度量. 在具协方差扰动模式下, 该文给出了回归系数和方差系数估计、最佳线性预测的局部影响诊断统计量.该结果与数据删除法进行了比较, 并通过实例进行了分析和说明.     

Allocating fixed costs or resources and setting targets via data envelopment analysis

In many applications of data envelopment analysis (DEA), there is often a fixed cost or input resource which should be imposed on all decision making units (DMUs). Cook and Zhu [W.D. Cook, J. Zhu, Allocation of shared costs among decision making units: A DEA approach, Computers and Operations Research 32 (2005) 2171-2178] propose a practical DEA approach for such allocation problems. In this paper, we prove that when some special constraints are added, Cook and Zhu’s approach probably has no feasible solution. The research of this paper focuses on two main aspects: to obtain a new fixed costs or resources allocation approach by improving Cook and Zhu’s approach, and to set fixed targets according to the amount of fixed resources shared by individual DMUs. When such special constraints are attached, our model is proved to be able to achieve a feasible costs or resources allocation. Numerical results for an example from the literature are presented to illustrate our approach.     

On principal Hessian directions for multivariate response regressions

We consider a multivariate response regression analysis with a vector of predictors. In this article, we develop the modification of principal Hessian directions based on principal components for estimating the central mean subspace without requiring a prespecified parametric model. We use a permutation test suggested by Cook and Yin (Aust New Z J Stat 43:147–199, 2001) for inference about the dimension. Simulation results and one real data are reported, and comparisons are made with four methods—most predictable variates, k-means inverse regression, optimal method of Yoo and Cook (Biometrika 94:231–242, 2007) and canonical correlation approach.     

基于pena距离的非线性回归模型的影响分析

基于pena距离统计量对非线性回归模型的影响分析进行了讨论,得到了非线性回归模型的pena距离公式,并对公式的分析性质以及其对高杠异常点的检测作用做出了相应的结论,得出了在一定条件下pena距离对异常点的检测优于Cook距离的结论,特别是对高杠杆异常点的检验,pena距离的效果更加明显,给出了实际数据检验结果,对方法的有效性进行了验证。     

数据矩阵条件指数的局部影响分析

以广义影响函数和广义Cook统计量为工具,考察对数据矩阵同时进行微小扰动在条件指数上产生的局部影响,导出了寻找条件指数最大影响方向的计算公式,并用一个实例说明该方法的应用．     

单纯形分布非线性模型的局部影响分析及其应用

讨论了单纯形分布非线性模型的局部影响分析问题.应用Cook(1986)的影响曲率方法研究了该模型关于微小扰动的局部影响,得到了局部影响分析的曲率度量.同时也应用PoonW Y和Poon Y S(1997)的保形法曲率方法研究了该模型的局部影响.对常见的扰动模型,分别进行了局部影响分析,得到了计算影响矩阵的简洁公式.最后还研究了两个实例,说明文中方法的应用价值.