ASSESSMENT OF LOCAL INFLUENCE IN MULTIVARIATE ANALYSIS

ＡＳＳＥＳＳＭＥＮＴＯＦＬＯＣＡＬＩＮＦＬＵＥＮＣＥＩＮＭＵＬＴＩＶＡＲＩＡＴＥＡＮＡＬＹＳＩＳ￥（石磊，王学仁）ＳｈｉＬｅｉ；ＷａｎｇＸｕｅｒｅｎ（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓｏｆＹｕｎｎａｎＰｒｏｖｉｎｃｅＤｅｐａｒ...     

ASSESSMENT OF LOCAL INFLUENCE IN MULTIVARIATE REGRESSION MODEL

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

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.     

ASSESSMENT OF LOCAL INFLUENCE ONCOX'S PROPORTIONAL HAZARDS MODEL

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

NUMERICAL METHODS FOR MAXWELL＇S EQUATIONS IN INHOMOGENEOUS MEDIA WITH MATERIAL INTERFACES

In this paper, we will present some recent results on developing numerical methods for solving Maxwell‘s equations in inhomogeneous media with material interfaces. First,we will present a second order upwinding embedded boundary method - a Cartesian grid based finite difference method with special upwinding treatment near the material interfaces. Second, we will present a high order discontinuous spectral element with Dubinar orthogonal polynomials on triangles. Numerical results on electromagnetic scattering and photonic waveguide will be included.     

VECTORIAL EKELAND＇S VARIATIONAL PRINCIPLE WITH A W-DISTANCE AND ITS EQUIVALENT THEOREMS

By using the properties of w-distances and Gerstewitz’s functions,we first give a vectorial Takahashi’s nonconvex minimization theorem with a w-distance.From this,we deduce a general vectorial Ekeland’s variational principle,where the objective function is from a complete metric space into a pre-ordered topological vector space and the perturbation contains a w-distance and a non-decreasing function of the objective function value.From the general vectorial variational principle,we deduce a vectorial Caristi’s fixed point theorem with a w-distance.Finally we show that the above three theorems are equivalent to each other.The related known results are generalized and improved.In particular,some conditions in the theorems of [Y.Araya,Ekeland’s variational principle and its equivalent theorems in vector optimization,J.Math.Anal.Appl.346(2008),9-16] are weakened or even completely relieved.     

PRICING EUROPEAN OPTION IN A DOUBLE EXPONENTIAL JUMP-DIFFUSION MODEL WITH TWO MARKET STRUCTURE RISKS AND ITS COMPARISONS

Using Fourier inversion transform, P.D.E. and Feynman-Kac formula, the closedform solution for price on European call option is given in a double exponential jump-diffusion model with two different market structure risks that there exist CIR stochastic volatility of stock return and Vasicek or CIR stochastic interest rate in the market. In the end, the result of the model in the paper is compared with those in other models, including BS model with numerical experiment. These results show that the double exponential jump-diffusion model with CIR-market structure risks is suitable for modelling the real-market changes and very useful.     

A PREDATOR-PREY SYSTEM WITH STAGE STRUCTURE AND HARVESTING FOR PREDATOR

In this paper, we consider a predator-prey system with stage structure and harvesting (where the predator population has two stages, an immature stage and a mature stage with harvesting, and the growth of the prey population is of Lotka-Volterra nature). We obtain the conditions of the globally asymptotic stability for three nonne-gative equilibria of this system.     

NECESSARY AND SUFFICIENT CONDITIONS OF A PLANE QUARTIC SYSTEM WITH DULAC＇S CENTER

ＮＥＣＥＳＳＡＲＹＡＮＤＳＵＦＦＩＣＩＥＮＴＣＯＮＤＩＴＩＯＮＳＯＦＡＰＬＡＮＥ　ＱＵＡＲＴＩＣＳＹＳＴＥＭＷＩＴＨＤＵＬＡＣ＇ＳＣＥＮＴＥＲＬｉＸｕｅｍｉｎ（李学敏）（ＳｈａｎｄｏｎｇＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，山东师范大学，邮编：２５００１...     

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.     

具有Rao简单结构的多元t-模型的MLE及其精确分布

探求模型中未知参数的估计及其分布一直是统计学研究中的感兴趣的问题.本文研究了具有Rao简单结构多元t-模型的极大似然估计, 利用条件分布方法,获得了其精确分布.     

具有Rao简单结构的多元t-模型的MLE的数字特征

本文在文[7]已求得未知参数MLEs的基础上，利用条件期望方法，研究了具有Rao简单结构多元t-模型的极大似然估计的数字特征．     

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.     

具有Rao简单结构的多元t-模型的参数区间估计

在统计推断中,模型中未知参数的区间估计是一个重要的研究内容.本文通过构造枢轴量研究了具有Rao简单结构多元￡-模型的参数区间估计,利用条件分布技巧,得到枢轴量的分布,从而获得模型中单个未知参数的置信区域以及参数的联合置信区域.     

线性等式约束下多元线性模型的简单投影预测

研究线性等式约束下一般生长曲线模型的简单投影预测θCSPP关于协方差阵的稳健性,得到θCSPP为条件线性可预测变量的条件最优线性无偏预测的充要条件,推广Bolfarine H等的有关结果。     

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。