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.     

局部影响分析中的一种新二阶方法

本文通过考察一种新影响图的保形法曲率,给出一种新二阶局部影响分析方法,并通过实例验证了该方法的有效性.     

GARCH模型的贝叶斯局部影响分析及其应用

广义自回归条件异方差(GARCH)模型能够很好地刻画金融资产收益二阶矩的相依关系,因此在金融时间序列中受到了广泛的应用。在GARCH模型的框架下,本文利用贝叶斯局部影响分析来评价先验、个体观测和样本分布的微小扰动的影响,利用扰动模型来刻画不同类型的扰动形式。我们构建了扰动模型的贝叶斯扰动形式,计算其几何量来表征扰动模型的内部结构。基于几个目标函数,本文利用几个不同的局部影响测量来量化不同扰动的程度。数值模拟研究验证了所提方法的有限样本表现。对纽约证券交易所综合指数(NYSE)和标准普尔500指数的GARCH建模说明了所提方法在实例研究中的有效性。     

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．     

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.     

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．     

广义非线性模型的影响分析

本文从几何的观点研究广义非线性模型及其影响分析，我们给出了均值漂移模型的曲率度量；在此基础上，导广义非线性模型度量影响的诊断统计量的二阶近似公式，作为推论，本文的结果适用于两种重要的特殊情形，第一，广义线性模型的影响分析，第二，正态非线性模型的影响分析。     

一般形式下的协方差分析模型的局部影响分析

利用局部影响的方法对一般形式下的协方差分析模型进行了讨论.把数据点或数据子集的扰动拓展到更广泛的扰动模式并进行了局部影响评价,导出了一般形式下的协方差分析模型在方差扰动下局部影响的曲率度量.     

单纯形分布模型的统计诊断

该文讨论了单纯形分布广义线性模型和广义非线性模型的影响分析问题, 得到了若干有用的诊断统计量;证明了数据删除模型和均值漂移模型的的等价性定理.同时还研究了该模型的变离差检验,得到了Score检验统计量.最后给出了两个实例, 说明该文方法的应用价值.     

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.     

Local influence analysis for semiparametric reproductive dispersion nonlinear models

The present paper proposes a semiparametric reproductive dispersion nonlinear model (SRDNM) which is an extension of the nonlinear reproductive dispersion models and the semiparameter regression models. Maximum penalized likelihood estimates (MPLEs) of unknown parameters and nonparametric functions in SRDNM are presented. Assessment of local influence for various perturbation schemes are investigated. Some local influence diagnostics are given. A simulation study and a real example are used to illustrate the proposed methodologies.     

非线性再生散度模型基于统计曲率的诊断统计量

对非线性散度模型在Euclid空间建立几何结构。在此基础上，研究了均值漂移模型的曲率度量。从而导出相应Cook距离，似然距离等诊断统计量的二阶近似公式。     

Assessment of local influence on Cox’s proportional hazards model

The second order approach of local influence (see [15]) is developed and applied to Cox’s proportional hazards model, and compared with Cook's local influence approach (see [6] and [13]) which was used in this model. To study local influence, we perturb not only all cases simultaneously, but also cases individually to obtain “direction curvature” in directionl and “curvature” for single case. Some examples are used to illustrate these methods. This work is supported by the Youth Science Foundation of Peking University and a research grant from State Educational Committee     

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     

ASSESSING LOCAL PRIOR INFLUENCE IN BAYESIAN ANALYSIS

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WFQEM‐based perturbation approach and its applications in analyzing nonlinear periodic structures

Based on the weak form quadrature element method, a perturbation approach is developed. Waves propagating in periodic beams on a nonlinear elastic foundation are studied by using the new proposed method. The feasibility and accuracy of the proposed method are verified by comparing the present results with those available in literatures in linear cases. Detailed modal analysis of the linear cases is conducted in order to obtain the dispersion relations of the nonlinear cases. The theoretical results show that the dispersion relations of the nonlinear cases are amplitude dependent. Furthermore, the effects of geometric parameters and degree of nonlinearity on the amplitude‐dependent dispersion relations are discussed in detail. This work provides a new method for analyzing the dispersion relations of nonlinear periodic structures and gives some useful guidelines for designing periodic beams or pipelines with nonlinear structure–foundation interaction. Copyright © 2016 John Wiley & Sons, Ltd.     

A geometric characterization of the nonlinear Schrodinger equation and its applications

We prove that the nonlinear Schrodinger equation of attractive type (NLS+ describes just spher-ical surfaces (SS) and the nonlinear Schrodinger equation of repulsive type (NLS-) determines only pseudo-spherical surfaces (PSS). This implies that, though we show that given two differential PSS (resp. SS) equationsthere exists a local gauge transformation (despite of changing the independent variables or not) which trans-forms a solution of one into any solution of the other, it is impossible to have such a gauge transformationbetween the NLS+ and the NLS-.