A recent method for assessing the local influence is introduced by Cook(1986), in which the normal curvature of the influence graph based on the likelihood displacement is used to monitor the influence of small pertur...A recent method for assessing the local influence is introduced by Cook(1986), in which the normal curvature of the influence graph based on the likelihood displacement is used to monitor the influence of small perturbation. Since then this method has been applied to various kind of models. However, the local influence in multivariate analysis is still an unexplored area because the influence for many statistics in multivariate analysis is not convenient to handle based on the Cook's likelihood displacement. In this paper, we suggest a method with a slight modification in Cook's approach to assess the local influence of small perturbation on a certain statistic. The local influence of the perturbation on eigenvalue and eigenvector of variance-covariance matrix in theoretical and sample version is assessed, some results for the other statistics in multivariate analysis such as generalized variance, canonical correlations are studied. Finally, two examples are analysed for illustration.展开更多
In this paper, we study local influence analysis for Zhang's generalized correlation coefficients and Hotelling's generalized correlation coefficient by using approach. of local influence analysis suggested by...In this paper, we study local influence analysis for Zhang's generalized correlation coefficients and Hotelling's generalized correlation coefficient by using approach. of local influence analysis suggested by Shi (1991), i.e., generalized influence function (GIF) and generalized Cook distance (GCD). An example is given to illustrate our results.展开更多
The amount of explained variation R2 is an overall measure used to quantify the information in a model and especially how useful the model might be when predicting future observations, explained variation is useful in...The amount of explained variation R2 is an overall measure used to quantify the information in a model and especially how useful the model might be when predicting future observations, explained variation is useful in guiding model choice for all types of predictive regression models, including linear and generalized linear models and survival analysis. In this work we consider how individual observations in a data set can influence the value of various R2 measures proposed for survival analysis including local influence to assess mathematically the effect of small changes. We discuss methodologies for assessing influence on Graf et al.'s R2G measure, Harrell's C-index and Nagelkerke's R2N. The ideas are illustrated on data on 1391 patients diagnosed with Diffuse Large B-cell Lymphoma (DLBCL), a major subtype ofNon-Hodgkin's Lymphoma (NHL).展开更多
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 pena...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.展开更多
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...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 direction and 'curvature' for single case. Some examples are used to illustrate these methods.展开更多
A general method for assessing local influence of minor perturbations of prior in Bayesian analysis is developed in this paper. U8ing some elementary ideas from differelltial geometryl we provide a unified approach fo...A general method for assessing local influence of minor perturbations of prior in Bayesian analysis is developed in this paper. U8ing some elementary ideas from differelltial geometryl we provide a unified approach for handling a variety of problexns of local prior influence. AS applications, we discuss the local influence of small perturbstions of normal-gamma prior density in linear model and investigate local prior influence from the predictive view.展开更多
In this paper,a unified diagnostic method for the nonlinear models with random effects based upon the joint likelihood given by Robinson in 1991 is presented.It is shown that the case deletion model is equivalent to t...In this paper,a unified diagnostic method for the nonlinear models with random effects based upon the joint likelihood given by Robinson in 1991 is presented.It is shown that the case deletion model is equivalent to the mean shift outlier model.From this point of view,several diagnostic measures,such as Cook distance,score statistics are derived.The local influence measure of Cook is also presented. A numerical example illustrates that the method is available.展开更多
This paper presents a unified diagnostic method for exponential nonlinear models with random effects based upon the joint likelihood given by Robinson in 1991. The authors show that the case deletion model is equivale...This paper presents a unified diagnostic method for exponential nonlinear models with random effects based upon the joint likelihood given by Robinson in 1991. The authors show that the case deletion model is equivalent to mean shift outlier model. From this point of view, several diagnostic measures, such as Cook distance, score statistics are derived. The local influence measure of Cook is also presented. Numerical example illustrates that our method is available.展开更多
Identifying influential nodes in complex networks and ranking their importance plays an important role in many fields such as public opinion analysis, marketing, epidemic prevention and control. To solve the issue of ...Identifying influential nodes in complex networks and ranking their importance plays an important role in many fields such as public opinion analysis, marketing, epidemic prevention and control. To solve the issue of the existing node centrality measure only considering the specific statistical feature of a single dimension, a SLGC model is proposed that combines a node’s self-influence, its local neighborhood influence, and global influence to identify influential nodes in the network. The exponential function of e is introduced to measure the node’s self-influence;in the local neighborhood,the node’s one-hop neighboring nodes and two-hop neighboring nodes are considered, while the information entropy is introduced to measure the node’s local influence;the topological position of the node in the network and the shortest path between nodes are considered to measure the node’s global influence. To demonstrate the effectiveness of the proposed model, extensive comparison experiments are conducted with eight existing node centrality measures on six real network data sets using node differentiation ability experiments, susceptible–infected–recovered(SIR) model and network efficiency as evaluation criteria. The experimental results show that the method can identify influential nodes in complex networks more accurately.展开更多
In this paper, we present influence analysis that can identify observations: which locally infulence the choice of smoothing parameter by cross-validation method when fitting a kelnel regnssion model. The diagnostic m...In this paper, we present influence analysis that can identify observations: which locally infulence the choice of smoothing parameter by cross-validation method when fitting a kelnel regnssion model. The diagnostic methods are illustrated with examples.展开更多
Nonignorable missing data are frequently encountered in various settings, such as economics,sociology and biomedicine. We review statistical inference for nonignorable missing-data problems, including estimation, infl...Nonignorable missing data are frequently encountered in various settings, such as economics,sociology and biomedicine. We review statistical inference for nonignorable missing-data problems, including estimation, influence analysis and model selection. For estimation of meanfunctionals, we review semiparametric method and empirical likelihood (EL) approach. For estimation of parameters in exponential family nonlinear structural equation models, we introduceexpectation-maximisation algorithm, Bayesian approach, and Bayesian EL method. For influenceanalysis, we investigate the case-deletion method and local influence analysis method fromthe frequentist and Bayesian viewpoints. For model selection, we present the modified Akaikeinformation criterion and penalised method.展开更多
In this paper, we consider the interaction between cases from the view of influence analysis in linear regression model. Our new diagnostic statistics can reveal the masking phenomenen in the situation of multiple out...In this paper, we consider the interaction between cases from the view of influence analysis in linear regression model. Our new diagnostic statistics can reveal the masking phenomenen in the situation of multiple outliers,and the method can also be adapted to the influential analysis in a general model based on single case deletion diagnostic and local influence approach,therefore has a wide range of application.展开更多
文摘A recent method for assessing the local influence is introduced by Cook(1986), in which the normal curvature of the influence graph based on the likelihood displacement is used to monitor the influence of small perturbation. Since then this method has been applied to various kind of models. However, the local influence in multivariate analysis is still an unexplored area because the influence for many statistics in multivariate analysis is not convenient to handle based on the Cook's likelihood displacement. In this paper, we suggest a method with a slight modification in Cook's approach to assess the local influence of small perturbation on a certain statistic. The local influence of the perturbation on eigenvalue and eigenvector of variance-covariance matrix in theoretical and sample version is assessed, some results for the other statistics in multivariate analysis such as generalized variance, canonical correlations are studied. Finally, two examples are analysed for illustration.
文摘In this paper, we study local influence analysis for Zhang's generalized correlation coefficients and Hotelling's generalized correlation coefficient by using approach. of local influence analysis suggested by Shi (1991), i.e., generalized influence function (GIF) and generalized Cook distance (GCD). An example is given to illustrate our results.
文摘The amount of explained variation R2 is an overall measure used to quantify the information in a model and especially how useful the model might be when predicting future observations, explained variation is useful in guiding model choice for all types of predictive regression models, including linear and generalized linear models and survival analysis. In this work we consider how individual observations in a data set can influence the value of various R2 measures proposed for survival analysis including local influence to assess mathematically the effect of small changes. We discuss methodologies for assessing influence on Graf et al.'s R2G measure, Harrell's C-index and Nagelkerke's R2N. The ideas are illustrated on data on 1391 patients diagnosed with Diffuse Large B-cell Lymphoma (DLBCL), a major subtype ofNon-Hodgkin's Lymphoma (NHL).
基金Supported by the National Natural Science Foundation of China (No. 10961026, 10761011)the National Social Science Foundation of China (No. 10BTJ001)
文摘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.
文摘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 direction and 'curvature' for single case. Some examples are used to illustrate these methods.
文摘A general method for assessing local influence of minor perturbations of prior in Bayesian analysis is developed in this paper. U8ing some elementary ideas from differelltial geometryl we provide a unified approach for handling a variety of problexns of local prior influence. AS applications, we discuss the local influence of small perturbstions of normal-gamma prior density in linear model and investigate local prior influence from the predictive view.
基金The research project supported by NSFC(1 9631 0 4 0 ) and NSFJ
文摘In this paper,a unified diagnostic method for the nonlinear models with random effects based upon the joint likelihood given by Robinson in 1991 is presented.It is shown that the case deletion model is equivalent to the mean shift outlier model.From this point of view,several diagnostic measures,such as Cook distance,score statistics are derived.The local influence measure of Cook is also presented. A numerical example illustrates that the method is available.
文摘This paper presents a unified diagnostic method for exponential nonlinear models with random effects based upon the joint likelihood given by Robinson in 1991. The authors show that the case deletion model is equivalent to mean shift outlier model. From this point of view, several diagnostic measures, such as Cook distance, score statistics are derived. The local influence measure of Cook is also presented. Numerical example illustrates that our method is available.
基金Project supported by the Natural Science Basic Research Program of Shaanxi Province of China (Grant No. 2022JQ675)the Youth Innovation Team of Shaanxi Universities。
文摘Identifying influential nodes in complex networks and ranking their importance plays an important role in many fields such as public opinion analysis, marketing, epidemic prevention and control. To solve the issue of the existing node centrality measure only considering the specific statistical feature of a single dimension, a SLGC model is proposed that combines a node’s self-influence, its local neighborhood influence, and global influence to identify influential nodes in the network. The exponential function of e is introduced to measure the node’s self-influence;in the local neighborhood,the node’s one-hop neighboring nodes and two-hop neighboring nodes are considered, while the information entropy is introduced to measure the node’s local influence;the topological position of the node in the network and the shortest path between nodes are considered to measure the node’s global influence. To demonstrate the effectiveness of the proposed model, extensive comparison experiments are conducted with eight existing node centrality measures on six real network data sets using node differentiation ability experiments, susceptible–infected–recovered(SIR) model and network efficiency as evaluation criteria. The experimental results show that the method can identify influential nodes in complex networks more accurately.
文摘In this paper, we present influence analysis that can identify observations: which locally infulence the choice of smoothing parameter by cross-validation method when fitting a kelnel regnssion model. The diagnostic methods are illustrated with examples.
基金This work was supported by the grants from the National Natural Science Foundation of China(Grant No.:11671349)the Key Projects of the National Natural Science Foundation of China(Grant No.:11731101).
文摘Nonignorable missing data are frequently encountered in various settings, such as economics,sociology and biomedicine. We review statistical inference for nonignorable missing-data problems, including estimation, influence analysis and model selection. For estimation of meanfunctionals, we review semiparametric method and empirical likelihood (EL) approach. For estimation of parameters in exponential family nonlinear structural equation models, we introduceexpectation-maximisation algorithm, Bayesian approach, and Bayesian EL method. For influenceanalysis, we investigate the case-deletion method and local influence analysis method fromthe frequentist and Bayesian viewpoints. For model selection, we present the modified Akaikeinformation criterion and penalised method.
文摘In this paper, we consider the interaction between cases from the view of influence analysis in linear regression model. Our new diagnostic statistics can reveal the masking phenomenen in the situation of multiple outliers,and the method can also be adapted to the influential analysis in a general model based on single case deletion diagnostic and local influence approach,therefore has a wide range of application.