Local influence in elliptical linear regression models

Abstract

Influence diagnostic methods are extended in this paper to elliptical linear models. These include several symmetric multivariate distributions such as the normal, Student t-, Cauchy and logistic distributions, among others. For a particular perturbation scheme and for the likelihood displacement the diagnostics agree with those developed for the normal linear regression model by Cook when the coefficients and the scale parameter are treated separately. This result shows the invariance of the diagnostics with respect to the induced model in the elliptical linear family. However, if the coefficients and the scale parameter are treated jointly we have a different diagnostic for each induced model, which makes this approach helpful for selecting the less sensitive model in the elliptical linear family. An example on the salinity of water is given for illustration.