一类非线性双曲型方程的广义Galerkin方法

本文研究一类非线性双曲型方程混合问题的广义Galerkin方法,即广义差分法.本文应用分片线性试探函数空间和分片常数检验函数空间,讨论了非线性二维二阶双曲型问题半离散和全离散方程的收敛性和稳定性,得到了与线性有限元方法相同的最优收敛阶.     

基于连续可分的广义非线性纵向数据模型偏离名义离差的score检验及其功效

指数族非线性模型或广义非线性模型是广义线性模型和正态回归模型的自然推广.本文针对可分的连续型指数族回归模型(如正态模型,Γ模型,逆高斯模型),讨论广义非线性纵向数据模型中偏离名义离差的检验问题,得到了检验的score统计量,并推导了它们的渐近分布和局部近似功效.然后利用Monte Carlo方法研究了检验统计量的性质.最后利用百慕大草地数据说明了检验方法的应用.     

一类非线性抛物型方程的广义Galerkin方法

本文研究一类非线性二维二阶抛物型方程混合问题的广义Galerkin方法(即广义差分法)讨论了半离散化和全离散化方程的收敛性和稳定性,并得到与有限元方法相同的最佳收敛阶。     

非线性结构向量自回归因果图的广义似然比辨识方法

利用图模型方法研究非线性结构向量自回归模型的因果性问题.构建了非线性结构向量自回归因果图模型,提出图模型因果性的广义似然比辨识方法.构造同期因果关系和滞后因果关系的广义似然比统计量,使用bootstrap方法来确定检验统计量的原分布,模拟研究论述了方法的有效性.     

带有指数型非线性项的离散泊松方程和热方程

该文主要利用单调迭代法和比较原理研究了带有指数型非线性项的离散泊松方程和带有指数型非线项的离散热方程解的存在性之间的关系,主要给出了带有指数型非线性项的离散泊松方程解存在时,带有指数型非线项的离散热方程解的渐近稳定性.     

非线性离散系统的一种实时建模方法

本文利用二维线性离散系统理论给出了非线性离散系统的一种实时建模方法,理 论及仿真实验显示这种实时模型能够任意逼近非线性离散动态.     

Hale中立型延迟微分方程的耗散性:新的准则及其应用

本文研究由Hale型非线性中立型延迟微分方程(HNDDEs)生成的耗散动力系统的耗散性,其与不变测度紧密相关.利用广义的Halanay不等式,给出了非线性非自治HNDDEs-些新的、有用的耗散准则.本文详细讨论了两个具体的动力系统:一是由传输线问题所产生的模型,二是非线性Nicholson丽蝇模型.     

一种新的振荡型DGPM(1,N|sin)模型及其应用

针对传统多变量灰色模型未能有效预测振荡序列的问题,提出一种新的振荡型DGPM(1,N|sin)模型.首先,将非线性时间周期项和时变参数引入离散灰色预测模型;然后,建立非线性规划模型,利用遗传算法确定最优参数;最后,将该模型应用于中国消费价格指数的预测中,验证了本文模型的有效性和适用性.结果显示,振荡型DGPM(1,N|sin)模型有较高的预测精度,为振荡序列的预测提供了有效方法.     

一类时滞Lipschitz非线性离散广义系统观测器的设计

针对一类时滞Lipschitz非线性离散广义系统,主要研究了系统的观测器设计问题.首先,基于广义系统的特殊结构对时滞广义系统进行变换,将系统转化为易于求取观测器的形式;其次,考虑到系统中的Lipschitz非线性项,将系统分两种情况并分别设计出了系统的观测器;最后,为保证系统与观测器的误差系统渐近稳定,通过利用线性矩阵不等式(LMI)的方法给出了两个观测器存在的条件,并通过数值例子验证了观测器设计方法的有效性.     

指数族广义非线性随机系数模型的变离差检验

指数族广义非线性随机系数模型是Smith &; Heitjan［１０］和 Wei et al［１１］所研究模型的推广。该文分别在模型离差 (dispersion) 的权不变和变异时，讨论了指数族 广义非线性随机系数模型的变离差的检验问题，得到了score检验统计量。并利用欧洲野兔数据，分别对正态分布模型、Γ 分布模型和 逆高斯分布模型说明检验方法的有效性。     

TESTING FOR VARYING DISPERSION OF LONGITUDINAL BINOMIAL DATA IN NONLINEAR LOGISTIC MODELS WITH RANDOM EFFECTS

In this paper, it is discussed that two tests for varying dispersion of binomial data in the framework of nonlinear logistic models with random effects, which are widely used in analyzing longitudinal binomial data. One is the individual test and power calculation for varying dispersion through testing the randomness of cluster effects, which is extensions of Dean(1992) and Commenges et al (1994). The second test is the composite test for varying dispersion through simultaneously testing the randomness of cluster effects and the equality of random-effect means. The score test statistics are constructed and expressed in simple, easy to use, matrix formulas. The authors illustrate their test methods using the insecticide data (Giltinan, Capizzi & Malani (1988)).     

恰当散度非线性模型变离差的检验

本文研究了恰当散度非线性模型变离差的检验问题.基于似然比统计量和得分统计量,得到变离差的检验.并且用数值例子说明方法是有效的.     

在非线性回归模型中误差为AR(2)的相关性检验

本文讨论了在非线性回归模型中误差为AR(2)的相关性检验，得到了误差相关性检验的似然比检验统计量、Score检验统计量．对感兴趣参数和多余参数，利用Cox and Reid(1987)提出的正交化方法，给出了修正的似然比检验统计量和Score检验统计量．推广了胡跃清，韦博成(1994)讨论的在非线性回归模型中误差为AR(1)相关性检验的结果．     

Testing for Varying Dispersion in Exponential Family Nonlinear Models

A diagnostic model and several new diagnostic statistics are proposed for testing for varying dispersion in exponential family nonlinear models. A score statistic and an adjusted score statistic based on Cox and Reid (1987, J. Roy. Statist. Soc. Ser. B, 55, 467-471) are derived in normal, inverse Gaussian, and gamma nonlinear models. An adjusted likelihood ratio statistic is also given for normal and inverse Gaussian nonlinear models. The results of simulation studies are presented, which show that the adjusted tests keep their sizes better and are more powerful than the ordinary tests.     

On Markov chain Monte Carlo Algorithms for Computing Conditional Expectations Based on Sufficient Statistics

Much work has focused on developing exact tests for the analysis of discrete data using log linear or logistic regression models. A parametric model is tested for a dataset by conditioning on the value of a sufficient statistic and determining the probability of obtaining another dataset as extreme or more extreme relative to the general model, where extremeness is determined by the value of a test statistic such as the chi-square or the log-likelihood ratio. Exact determination of these probabilities can be infeasible for high dimensional problems, and asymptotic approximations to them are often inaccurate when there are small data entries and/or there are many nuisance parameters. In these cases Monte Carlo methods can be used to estimate exact probabilities by randomly generating datasets (tables) that match the sufficient statistic of the original table. However, naive Monte Carlo methods produce tables that are usually far from matching the sufficient statistic. The Markov chain Monte Carlo method used in this work (the regression/attraction approach) uses attraction to concentrate the distribution around the set of tables that match the sufficient statistic, and uses regression to take advantage of information in tables that “almost” match. It is also more general than others in that it does not require the sufficient statistic to be linear, and it can be adapted to problems involving continuous variables. The method is applied to several high dimensional settings including four-way tables with a model of no four-way interaction, and a table of continuous data based on beta distributions. It is powerful enough to deal with the difficult problem of four-way tables and flexible enough to handle continuous data with a nonlinear sufficient statistic.     

Testing over-representation of observations in subsets of a DEA technology

This paper proposes a test for whether data are over-represented in a given production zone, i.e. a subset of a production possibility set which has been estimated using the non-parametric Data Envelopment Analysis (DEA) approach. A binomial test is used that relates the number of observations inside such a zone to a discrete probability weighted relative volume of that zone. A Monte Carlo simulation illustrates the performance of the proposed test statistic and provides good estimation of both facet probabilities and the assumed common inefficiency distribution in a three dimensional input space. Potential applications include tests for whether benchmark units dominate more (or less) observations than expected.     

GARCH模型参数变化的残量检验

本文研究GARCH模型参数变化的检验问题. 给出残量累积和统计量, 在原假设下得到了统计量的极限分布; 模拟结果表明残量检验可以弥补Kim, Cho和Lee (2000)\ucite{1}提出的平方累积和检验的某些不足, 比如经验势函数值过低的问题.     

具有ARIMA(0,1,0)误差的非线性模型的异方差检验

本文讨论随机误差是 ARIMA( 0 ,1 ,0 )序列的非线性回归模型的异方差检验问题 .首先导出了检验的 score统计量 ,然后利用参数的正交变换 ,得到了调整的 score统计量 .最后 ,利用氯化物数据 ( Bates &Watts,1 988)说明了检验方法的应用     

非线性均值方差模型的贝叶斯数据删除统计诊断

文章在非线性均值方差模型框架下基于K-L距离研究贝叶斯数据删除影响的统计诊断问题,通过应用Gibbs抽样和MH算法估计贝叶斯数据删除影响诊断统计量.随机模拟研究和红鳟鲑鱼数据的数值例子说明该诊断方法的可行性.     

Towards data driven selection of a penalty function for data driven Neyman tests

The data driven Neyman statistic consists of two elements: a score statistic in a finite dimensional submodel and a selection rule to determine the best fitted submodel. For instance, Schwarz BIC and Akaike AIC rules are often applied in such constructions. For moderate sample sizes AIC is sensitive in detecting complex models, while BIC works well for relatively simple structures. When the sample size is moderate, the choice of selection rule for determining a best fitted model from a number of models has a substantial influence on the power of the related data driven Neyman test. This paper proposes a new solution, in which the type of penalty (AIC or BIC) is chosen on the basis of the data. The resulting refined data driven test combines the advantages of these two selection rules.