Abstract: 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 displace ment 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 multi variate 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 papers 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.

Key words: Multivariate Analysis, Normal curvature, perturbation scheme, Local Influence