ASSESSMENT OF LOCAL INFLUENCE IN MULTIVARIATE REGRESSION MODEL

1Intr0ductionRegressi0ndiagnosticsandinfluenceanalysis,asatechlliquetoinvestigatethefittingresu1t0fmodelandinfluentialpatternsinthedatasets,hadbeenpaidgreatattentioninrecentyears.Someworksweresummarizedinseveralb00ks(see[1]-[3l),muchofwhichemphasizedtlieidentilicati0nofinfiuentialpointsandinvo1vedde1etionofthedatacases.[4jemP1oyedlocalinfluenceana1ysisasana1ternativetechniquet0studytheidentificati0nofinfluentia1p0ints-inwhichtl1en0rma1curvature0finfluencegrapl1basedon1ikelih0oddisplacementatnu…     

LOCAL INFLUENCE ASSESSMENT IN A MULTIVARIATE t-MODEL WITH RAO＇S SIMPLE STRUCTURE

The local influence analysis is an important problem in statistical inference and some models have been discussed in many literatures^[1- 5]. This paper deals with the problem of assessing local influences in a multivariate t-model with Rao‘s simple structure(RSS). Based on Cook‘s likelihood displacement, the effects of some minor perturbation on the statistical inference is assessed. As an application, a common covariance-weighted perturbation is thoroughly discussed.     

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.     

ASSESSMENT OF LOCAL INFLUENCE FOR GENERALIZED CORRELATION COEFFICIENTS

ＡＳＳＥＳＳＭＥＮＴＯＦＬＯＣＡＬＩＮＦＬＵＥＮＣＥＦＯＲＧＥＮＥＲＡＬＩＺＥＤＣＯＲＲＥＬＡＴＩＯＮＣＯＥＦＦＩＣＩＥＮＴＳ（陈建宝，陈涛）￥ＣｈｅｎＪｉａｎｂａｏＣｈｅｎＴａｏ（Ｄｅｐｔ．ｏｆＳｔａｔｉｓｔｉｃｓ，ＹｕｎｎａｎＵｎｉｖ，Ｋｕｎｍｉ...     

多元线性回归中的AP统计量和距离影响函数

本文对多元线性回归模型定义了AP统计量和距离影响函数;将它们分解为两项之积,指出强影响点、异常点、高杠杆点间的内在联系;讨论了上述三种点的探查方法.最后,给出与距离影响函数有关的一个定理.     

多元线性回归中度量影响的置信域体积比统计量

本文从多元线性回归模型回归系数的椭球置信域出发,导出度量影响的置信域体积比诊断统计量,并给出了它在协方差矩阵未知时的近似表达式。     

ASSESSMENT OF LOCAL INFLUENCE ONCOX'S PROPORTIONAL HAZARDS MODEL

1.IntroductionTheproportionalhazardsregressionmodelisasemiparametricmodel.Theloglikelihoodforthismodelisasumoverrisksets.Theperturbationofoneobservationedictsseveraloftheserisksets.Thus,theassessmentofcaseinfluenceismorecomplexforthismodelthanlinearandgeneralizedlinearmodels.TheglobalialluenceofindividualcaseonregressionparameterestimatesforCox'smodelhasbeenanalysedbyCainandLange[4],ReidandCrepeaull4],etal.TheideaofdtherentiationinsteadofdeletionisprominentinthelocalinduenceapproachofCook[…     

多元统计中期望向量的线性容许估计

设Ｙ１，Ｙ２，…，Ｙｎ独立同分布，ＥＹ１＝β，ＣｏｖＹ１＝Σ，这里β∈Ｒｍ与Σ：ｍ×ｍ＞０均未知．取Ｌ１（ｄ，β）＝（ｄ－β）′（ｄ－β），Ｌ２＝（ｄ，β）（ｄ－β）′，Ｌ＝｛Ｌ１Ｙ１＋Ｌ２Ｙ２＋…＋ＬｎＹｎ：Ｌｉ为ｍ阶实方阵，ｉ＝１，２，…，ｎ｝．本文在Ｌ１和Ｌ２下分别给出了线性估计在Ｌ中是β的容许估计的充要条件．     

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.     

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…     

多元线性模型中的有偏估计

刘金山在1999年给出了多元线性模型参数分量βi和参数矩阵B的有偏估计β1=(X'X)-1YCi,i=1,…,m和B=(β1,β2,…,βm)以及βi的性质.本文从另一角度得到了同样的估计,证明了刘金山文中所给的两个检验是UMP检验,估计βi是βi的线性可容许估计,证明了B不是B的可容许估计,由此给出了两种改进估计.     

多元正交小波包

本文利用Ｓｔｏｃｋｌｅｒ在引文（２）中所提供的多元小波矩阵描述的工具，将Ｃｈｕｉ在引文（１）中关于一元正交小波包的结果推广到多元正交小波包。     

多元Bernstein算子的导数与函数的光滑性

利用一个新的光滑性度量刻画多元Bernstein算子方向导数的特征,建立Bernstein算子的导数与逼近函数光滑性之间的等价关系。同时,一个关于一元Bernstein算子的相应结果被推广到多元情形。     

多元回归系数的所有k—容许估计

对于多元线性模型Y～N（XΘ，）（已知）中的可估函数SXΘ的估计问题，取损失函数为（δ－SXΘ）'（δ－SXΘ）．用风险函数矩阵的前k个顺序特征值之和作为比较不同估计的风险函数大小的标准，我们可定义所谓的"k－容许估计"．本文得到了SXΘ的线性估计AY＋D在一切估计类中k－容许的充要条件．     

MULTIVARIATE FOURIER SERIES OVER A CLASS OF NON TENSOR－PRODUCT PARTITION DOMAINS

This paper finds a way to extend the well-known Fourier methods,to so-called n 1 directions partition domains in n-dimension.In particular,in 2-D and 3-D cases,we study Fourier methods over 3-direction parallel hexagon partitions and 4-direction parallel paralleogram dodecahedron partitions,respectively.It has pointed that,the most concepts and results of Fourier methods on tensor-product case,such as periodicity,orthogonality of Fourier basis system,Partial sum of Fourier series and its approximation behavior,can be moved on the new non tensor-product partiton case.     

多重线性回归中数据联合影响的分解及数据的交叉影响

一、引言考虑多重线性回归模型Y=Xβ ε,(1)其中,Y=(y_1,…y_n_)′为 n×p 观察矩阵,X=(x_1,…,x_n)′为 n×(k 1)列满秩设计矩阵,β=(β_0,β_1,…β_k)′为(k 1)×p 未知参数矩阵,ε=(ε_1,…ε_n)′为 n×p 随机误差矩阵,ε_1…,ε_n 相互独立.     

地方总教育投资分配的博弈分析

本文采用博弈论研究地方总教育投资分配的模型 ,该模型包含两个地方政府和一个中央政府 ,并分别为地方政府提供决策 .首先 ,描述了基本模型 ,分别给出了地方政府的效用函数 ;接着分析了地方政府同时行动时的总教育投资分配 ,然后分析了地方政府顺序行动时的总教育投资分配 ;最后给出了最优解的算法并举例说明地方政府怎样去做决策     

任意剖分下的多元样条分析

本文采用代数几何的方法,研究了在任意剖分下多元样条函数的各种性质.定理2—4给出了一个函数S(υ,ν)是多元参数型样条的充分必要条件.定理1指出了多元样条函数具有“解析延拓”的特征性质.文中得到在任意剖分下多元样条的一般表达形式(定理9和10)和多元样条插值的一般理论.文中也讨论了多元有理样条函数.     

局部环上辛群在线性群中的扩群

本文完全定出了局部环上辛群在一般线性群中的扩群.     

ALTERNATIVE MEASURES OF THE EXPLANATORY POWER OF GENERAL MULTIVARIATE REGRESSION MODELS

In this paper R ²-type measures of the explanatory power of multivariate linear and categorical probit models proposed in the literature are reviewed and their deficiencies discussed. It is argued that a measure of the explanatory power should take into account the components which are explicitly modelled when a regression model is estimated while it should be indifferent to components not explicitly modelled. Based on this view three different measures for multivariate probit models are proposed. Results of a simulation study are presented, designed to compare two measures in various situations, to evaluate the BC _a bootstrap technique for testing the hypothesis that the corresponding measure is zero, and to calculate approximate confidence intervals. The BC _a bootstrap technique turned out to work quite well for a wide range of situations, but may lead to misleading results if the true values of the corresponding measure are close to zero.