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
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.
