The Frechet's metric as a measure of influence in multivariate linear models with random errors elliptically distributed

In general, the influence diagnostics are based on two aspects: the perturbation of the model and the comparison of the results. The most used scheme of perturbation is the omission of the cases and, generally, as a pattern of comparison, a metric is used. A sample version of the Frechet's metric is proposed to quantify the deviation between the sample distributions of the statistics. This is the way that a generic influence measure is obtained which can be applied to a great deal of statistical techniques. In particular, for linear multivariate models with random errors elliptically distributed, it is applied on the BLUE of the estimable linear functions.