Influential observations in the estimation of mean vector and covariance matrix

Statistical procedures designed for analysing multivariate data sets often emphasize different sample statistics. While some procedures emphasize the estimates of both the mean vector mu and the covariance matrix Sigma, others may emphasize only one of these two sample quantities. In effect, while an unusual observation in a data set has a deleterious impact on the results from an analysis that depends heavily on the covariance matrix, its effect when dependence is on the mean vector may be minimal. The aim of this paper is to develop diagnostic measures for identifying influential observations of different kinds. Three diagnostic measures, based on the local influence approach, are constructed to identify observations that exercise undue influence on the estimate of mu of Sigma, and of both together. Real data sets are analysed and results are presented to illustrate the effectiveness of the proposed measures.