非线性随机效应模型的异方差性检验

随机效应模型广泛应用于刻画重复测量数据的特征．在该模型中,随机误差的方差包括受试群体内部及受试群体之间两项方差．Ｚｈａｎｇ和 Ｗｅｉｓｓ ２０００年研究了线性随机效应模型的异方差检验,本文对非线性随机效应模型,分别讨论了群体内、群体间和多变量的异方差性的检验问题,得到了检验的ｓｃｏｒｅ统计量,并讨论了三种情形下,相应的ｓｃｏｒｅ函数之间的关系．最后给出一个数值例子说明上述方法的有用性．     

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     

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)).     

半参数非线性模型的统计诊断与影响分析

本文系统研究了半参数非线性回归模型的统计诊断与影响分析方法;得到了一系列诊断统计量,两个实际数值例子验证了本文给出的诊断方法的有效性。     

离散型指数族非线性模型的变离差检验

It is necessary to test for varying dispersion in generalized nonlinear models. Wei,et al (1998) developed a likelihood ratio test,a score test and their adjustments to test for varying dispersion in continuous exponential family nonlinear models. This type of problem in the framework of general discrete exponential family nonlinear models is discussed. Two types of varying dispersion, which are random coefficients model and random effects model, are proposed ,and corresponding score test statistics are constructed and expressed in simple ,easy to use ,matrix formulas.     

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.     

基于纵向数据的ZIP和ZIB非线性回归模型的随机效应存在性检验(英文)

本文研究了基于纵向数据的ZIP和ZIB模型的随机效应存在性检验问题.采用score检验方法,得到了,可用矩阵表示的score检验统计量.最后,用一个数据实例说明检验方法的有效性.     

无界区域R3上的非线性应变波方程与薛定谔方程藕合方程组的指数吸引子

本文研究了无界区域R~3上的非线性应变波方程与薛定谔方程藕合方程组.运用带权空间构造一类紧算子和算子分解的方法,得到了该方程在无界区域R3上的H~2×H~2×H~1(R~3)中拥有一个指数吸引子.     

TESTING OF CORRELATION AND HETEROSCEDASTICITY IN NONLINEAR REGRESSION MODELS WITH DBL（p,q, 1） RANDOM ERRORS

Chaos theory has taught us that a system which has both nonlinearity and random input will most likely produce irregular data. If random errors are irregular data, then random error process will raise nonlinearity （Kantz and Schreiber （1997））. Tsai （1986） introduced a composite test for autocorrelation and heteroscedasticity in linear models with AR（1） errors. Liu （2003） introduced a composite test for correlation and heteroscedasticity in nonlinear models with DBL（p, 0, 1） errors. Therefore, the important problems in regression model axe detections of bilinearity, correlation and heteroscedasticity. In this article, the authors discuss more general case of nonlinear models with DBL（p, q, 1） random errors by score test. Several statistics for the test of bilinearity, correlation, and heteroscedasticity are obtained, and expressed in simple matrix formulas. The results of regression models with linear errors are extended to those with bilinear errors. The simulation study is carried out to investigate the powers of the test statistics. All results of this article extend and develop results of Tsai （1986）, Wei, et al （1995）, and Liu, et al （2003）.     

TESTING OF CORRELATION AND HETEROSCEDASTICITY IN NONLINEAR REGRESSION MODELS WITH DBL(p,q,1) RANDOM ERRORS

Chaos theory has taught us that a system which has both nonlinearity and random input will most likely produce irregular data. If random errors are irregular data, then random error process will raise nonlinearity (Kantz and Schreiber (1997)). Tsai (1986) introduced a composite test for autocorrelation and heteroscedasticity in linear models with AR(1) errors. Liu (2003) introduced a composite test for correlation and heteroscedasticity in nonlinear models with DBL(p, 0, 1) errors. Therefore, the important problems in regres- sion model are detections of bilinearity, correlation and heteroscedasticity. In this article, the authors discuss more general case of nonlinear models with DBL(p, q, 1) random errors by score test. Several statistics for the test of bilinearity, correlation, and heteroscedas-ticity are obtained, and expressed in simple matrix formulas. The results of regression models with linear errors are extended to those with bilinear errors. The simulation study is carried out to investigate the powers of the test statistics. All results of this article extend and develop results of Tsai (1986), Wei, et al (1995), and Liu, et al (2003).     

关于集值映射的随机不动点的稳定性

本文研究随机集值映射不动点的稳定性。通过集值分析,得到了随机集值不动点的本质稳定集的存在性。在Baire分类意义下,大多数的随机集值映射的随机不动点都是本质稳定的。这些推广了现有文献中的相应结果。     

MODELING INDIVIDUAL TREE MORTALITY RATES USING MARGINAL AND RANDOM EFFECTS REGRESSION MODELS

Abstract Developing models to predict tree mortality using data from long‐term repeated measurement data sets can be difficult and challenging due to the nature of mortality as well as the effects of dependence on observations. Marginal (population‐averaged) generalized estimating equations (GEE) and random effects (subject‐specific) models offer two possible ways to overcome these effects. For this study, standard logistic, marginal logistic based on the GEE approach, and random logistic regression models were fitted and compared. In addition, four model evaluation statistics were calculated by means of K‐fold cross‐valuation. They include the mean prediction error, the mean absolute prediction error, the variance of prediction error, and the mean square error. Results from this study suggest that the random effects model produced the smallest evaluation statistics among the three models. Although marginal logistic regression accommodated for correlations between observations, it did not provide noticeable improvements of model performance compared to the standard logistic regression model that assumed impendence. This study indicates that the random effects model was able to increase the overall accuracy of mortality modeling. Moreover, it was able to ascertain correlation derived from the hierarchal data structure as well as serial correlation generated through repeated measurements.     

纵向数据下部分非线性模型的广义经验似然推断

本文研究了纵向数据下部分非线性模型中未知参数的置信域的构造.利用经验似然方法,构造了非线性函数中未知参数的广义对数经验似然比统计量,证明了其渐近于卡方分布.同时,得到了未知参数的最大经验似然估计,并证明了其渐近正态性.     

ON CONFIDENCE REGIONS OF SEMIPARAMETRIC NONLINEAR REGRESSION MODELS(A GEOMETRIC APPROACH)

1IntroductionSelltipaxanetricmodelsaxemodelscolltaillingbothparametricalldnonparametriccom-pOnents,wl1erethenol1parametriccomponentplaystheroleofanusianceparameter.Moreprecisely,asellliparametriclllodelisparameterizedbyaparameterofillteresttakingvaI1lesinfinite-din1el1sionajEuclidenspaceal1danusianceparantetertakingvaluesininfinite-dimellsionalspace.Tl1ismodelembodiesacolllpro11tisebetweenemployingagelleralnonparametricspeci-ficatioll.wl1ich,iftheconditiol1il1gvariablesarehighdimensional,woul…     

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．     

半参数广义线性混合效应模型的影响分析

本文把随机效应当作是缺失数据并利用P-样条拟合非参数部分,从而得到了半参数广义线性混合效应模型(GPLMM)的MCNR估计算法;同时利用Q-函数,我们得到了模型的参数部分的广义Cook距离以及非参数部分的广义DFIT,此外,本文还研究了四种不同扰动情形的PLMM的局部影响分析,得到了相应的影响矩阵,最后,我们通过—个实际例子验证了所提出的诊断统计量的有效性。     

多元协方差阵扰动模型岭估计的影响分析

本文研究了多元线性同归模型岭估计的影响分析问题.利用最小二乘估计方法,获得了多元协方差阵扰动模型与原模型参数阵之间的岭估计的一些关系式,给出了度量影响大小的基于岭估计的广义Cook距离.     

金融系统的非线性分析:交易量对股价波动的非线性影响

如何研究股价波动和成交量之间的关系一直是金融系统研究中感兴趣的话题.Lamoureux 和 Lastrapes 认为选择日交易量度量每天流入市场的信息量是合理的,但他们假定交易量对波动率的影响是线性的.提出部分非线性GARCH模型分析交易量对股票市场波动率的影响,基于GARCH模型局部线性化非参数似然估计方法,对中国证券市场股票价格和交易量数据进行实证研究.结果表明,交易量对股价波动的影响具有显著的非线性性.     

具有双线性BL(1,1,1,1)误差的非线性回归模型相关性和方差齐性的检验

在时间序列回归模型分析中,相关性和方差齐性的检验是一个很基本的问题.本文讨论了具有双线性BL(1,1,1,1)误差的非线性回归模型的相关性和方差齐性的检验问题, 用Score检验方法给出了双线性项检验、相关性检验、方差齐性检验、以及相关性和方差齐性同时检验的检验统计量.推广和发展了具有线性序列误差项回归模型的结果.本文还用数值实例说明了检验方法的实用价值.     

拟等级网格下非线性延迟微分方程间断有限元法

本文利用间断有限元法求解非线性延迟微分方程,在拟等级网格下.给出非线性延迟微分方程间断有限元解的整体收敛阶和局部超收敛阶,数值实验验证了理论结果的正确性.