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.     

具有Rao简单结构的多元T-模型的局部影响分析

本文应用以Kullback-Leibler散度为基础的Bayesian局部影响方法，对具有Rao简单结构的多元T-模型进行了局部影响分析．在确定了先验分布假设下，详细地研究了这个模型的Bayesian Hessian矩阵，作为应用，特别考虑了常见的加权协方差扰动形式．     

约束条件下线性模型协方差阵扰动的影响分析

该文研究了协方差阵扰动和数据删除对最佳线性无偏估计(BLUE)的影响问题, 给出了在约束条件下一般线性模型与在约束条件下Gauss-Markov模型及在约束条件下数据删除模型中回归参数β的BLUE之间的关系式. 作者还定义了度量影响大小的广义Cook距离D_V并给出了D_V的两个计算公式.     

多元线性回归置信域的局部影响

运用Ｃｏｏｋ（１９８６）的局部影响法评价多元线性回归模型的微小扰动对回归系数置信域的影响，扰动方式包括协方差阵扰动，自变量扰动和因变量扰动．     

具有均匀结构的多元$t$\,-模型的局部影响分析

本文研究具有均匀结构的多元$t$\,-模型的局部影响分析问题\bd 依据Cook的曲率度量, 我们考虑了微小扰动对统计推断的影响, 由此导出了局部影响分析中最为关心的统计量---最大曲率方向\bd作为一种应用, 本文还祥细讨论了常见的协方差加权扰动形式.     

协方差矩阵扰动生长曲线模型岭估计的影响分析

本文研究了协方差矩阵发生扰动时，生长曲线模型岭估计的影响分析，建立了生长曲线模型、协方差矩阵扰动生长曲线模型岭估计之间的关系式。讨论了协方差扰动和数据删除对岭估计的影响，导出了度量影响大小的基于岭估计的广义Cook距离Di^*（k）最后，用实例说明了用Di^*(k）度量生长曲线模型的影响点是有效的。     

基于M估计的线性混合模型的局部影响分析

对纵向数据的线性混合模型,用Fisher得分法得到了参数的M估计(稳健估计),给出了其渐近性质,利用影响曲率研究了M估计下的随机误差方差扰动的局部影响分析问题,并通过葡萄糖数据的实例进行了分析论证.     

Fusion框架系统的局部框架扰动的稳定性

该文在Hilbert空间中一般的框架序列扰动形式下,利用正交投影的性质和对偶框架的性质研究了原序列张成的闭子空间与扰动序列张成的闭子空间的关系,并探讨了局部框架的一般扰动对fusion框架系统稳定性的影响.这些结果推广和改进了由Casazza,Kutyniok和Li等得到的著名结果.     

基于线性回归的协方差分析模型与检验

基于虚拟变量和局部显著性检验,在线性回归的体系下重建了协方差分析理论,包括描述模型、估计参数、解释方差分解的不同形式及几何意义,得到了协方差分析的三个重要检验.还验证了响应变量校正的效果,证明了原数据中因素显著性与校正后数据中因素显著性之间的两种联系.     

多元$t$分布数据的局部影响分析

对于多元$t$分布数据, 直接应用其概率密度进行影响分析是困难的\bd 本文通过引入服从Gamma分布的权重, 将其表示为特定多元正态分布的混合\bd 在此基础上, 进而将权重视为缺失数据, 引入EM算法; 从而利用基于完全数据似然函数的条件期望进行局部影响分析\bd 本文进一步系统研究了加权扰动模型下的局部影响分析, 得到了相应的诊断统计量; 并通过两个实例说明了这种方法的有效性.     

Assessing Local Influence in Canonical Correlation Analysis

The first order local influence approach is adopted in this paper to assess the local influence of observations to canonical correlation coefficients, canonical vectors and several relevant test statistics in canonical correlation analysis. This approach can detect different aspects of influence due to different perturbation schemes. In this paper, we consider two different kinds, namely, the additive perturbation scheme and the case-weights perturbation scheme. It is found that, under the additive perturbation scheme, the influence analysis of any canonical correlation coefficient can be simplified to just observing two predicted residuals. To do the influence analysis for canonical vectors, a scale invariant norm is proposed. Furthermore, by choosing proper perturbation scales on different variables, we can compare the different influential effects of perturbations on different variables under the additive perturbation scheme. An example is presented to illustrate the effectiveness of the first order local influence approach.     

ASSESSMENT OF LOCAL INFLUENCE IN A GROWTH CURVE MODEL WITH RAO'S SIMPLE COVARIANCE STRUCTURE

The present paper deals with the problem of assessing the local influence in a growth curve model with Rao's simple covariance structure. Based on the likelihood displacement, the curvature measure is employed to evaluate the effects of some minor perturbations on the statistical inference, thus leading to the large curvature direction, which is the most critical diagnostic statistic in the context of the local influence analysis. As an application, the common covariance-weighted perturbation scheme is thoroughly considered.     

LOCAL INFLUENCE ASSESSMENT BASED ON LOCAL DIVERGENCE IN STOCHASTIC REGRESSION MODEL

Abstract. This paper describes the local influence assessment for parameter inferenceof a statistlcual model by using curvatures assoclated with Iota| divergence under ageneric perturbatlon scheme. The results are applied to examine the local influence instochastlc regresslon model under two perturbation schemes. An economic examp|e isanalyzed to ~llustrate results here.     

BAYESIAN LOCAL INFLUENCE ASSESSMENTS IN A GROWTH CURVE MODEL WITH GENERAL COVARIANCE STRUCTURE

1 IntroductionThe problem of how to deal With local influence assessment in a growth curve model withgeneral covariance structure is very important. There are two main reasons why this is so. First,although the growth curve model can be viewed as a generalizetion of classical linear regressionmodel in some wad, as pointed out by for etc.[1], two models are substantially different andthe former is much more complicated than the latter. Secondly3 it is not generally the case withlocally influen…     

混合线性模型效应参数的Bayes局部影响分析

该文研究混合线性模型效应参数的Ｂａｙｅｓ局部影响评价问题．导出了混合线性模型在各种扰动下效应参数的Ｂａｙｅｓ局部影响度量，并给出了平衡单向分类随机效应模型下的一些结果．最后通过实例分析，以证实该文方法的有效性．     

Local influence analysis of multivariate probit latent variable models

The multivariate probit model is very useful for analyzing correlated multivariate dichotomous data. Recently, this model has been generalized with a confirmatory factor analysis structure for accommodating more general covariance structure, and it is called the MPCFA model. The main purpose of this paper is to consider local influence analysis, which is a well-recognized important step of data analysis beyond the maximum likelihood estimation, of the MPCFA model. As the observed-data likelihood associated with the MPCFA model is intractable, the famous Cook's approach cannot be applied to achieve local influence measures. Hence, the local influence measures are developed via Zhu and Lee's [Local influence for incomplete data model, J. Roy. Statist. Soc. Ser. B 63 (2001) 111-126.] approach that is closely related to the EM algorithm. The diagnostic measures are derived from the conformal normal curvature of an appropriate function. The building blocks are computed via a sufficiently large random sample of the latent response strengths and latent variables that are generated by the Gibbs sampler. Some useful perturbation schemes are discussed. Results that are obtained from analyses of an artificial example and a real example are presented to illustrate the newly developed methodology.     

Local influence in multilevel regression for growth curves

Influence analysis is important in modelling and identification of special patterns in the data. It is well established in ordinary regression. However, analogous diagnostics are generally not available for the multilevel regression model, in which estimation involves a complex iterative algorithm. This paper studies the local influence of small perturbations on the parameter estimates in the multilevel regression model with application to growth curves. The estimation is based on the iterative generalized least-squares (IGLS) method suggested by Goldstein (Biometrika 73 (1986) 43). The generalized influence function and generalized Cook statistic (Biometrika 84(1) (1997) 175) of IGLS of unknown parameters under some specific simultaneous perturbations are derived to study the joint influence of subject units on parameter estimators. The perturbation scheme is introduced through a variance–covariance matrix of error variables. A one-step approximation formula is suggested for simplifying the computations. The method is examined on growth-curve data.     

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.