SECOND ORDER LOCAL INFLUENCE IN LINEAR DISCRIMINANT ANALYSIS

We adapt the local influence method to linear discriminant analysis for the purpose of investigating the influence of observations. A simultaneous perturbation on all observations coming from two populations is considered. We study the curvatures and the associated direction vectors of the surface formed by the perturbed maximum likelihood estimators of parameters of interest, in addition to the direction vector of the maximum slope. We show that the influence function method gives essentially the same information as the direction vector of the maximum slope. A numerical example illustrates that the local influence method gives valuable information about influential observations and outliers, even when the influence function method and the case deletion method are not adequate.