Local Influence and Leverage in Elliptical Nonlinear Regression Models

Abstract: This work deals with the calculation of local influence curvatures and generalized leverage in univariate elliptical nonlinear regression models. This class of models includes all symmetric continuous distributions, such as normal, Student-t, generalized Student-t, exponential power and logistic, among others. We derive the total local influence of the ith observation Ci and we decompose the generalized leverage matrix into two terms, one that may be interpreted as a contribution of the position parameter estimates on the leverage and the other as a kind of correction due to the estimation of the dispersion parameter. This correction vanishes for the normal case. We also establish a connection between generalized leverage and local influence. An illustrative example is given