Designs with High Breakdown Point in Nonlinear Models

Abstract

Least trimmed squares estimators are outlier robust since they have a high breakdown point because of trimming large residuals. But the breakdown point depends also on the design. In generalized linear models and nonlinear models, the connection between breakdown point and design is given by the fullness parameter defined by Vandev and Neykov (1998). As Müller and Neykov (2003) have shown, this fullness parameter is given in generalized linear models by the largest subdesign where the parameter of interest is not identifiable. In this paper, we show that this connection does not hold for all nonlinear models. This means that the identifiability at subdesigns cannot be used for finding designs which provide high breakdown points. Instead of this, the fullness parameter itself must be determined. For some nonlinear models with two parameters, the fullness parameter is derived here. It is shown that the fullness parameter and thus a lower bound for the breakdown point depends heavily on the design and the parameter space.