An Alternative Definition of Finite-Sample Breakdown Point with Applications to Regression Model Estimators

Abstract

We propose an alternative definition of the finite-sample breakdown point. This breakdown point is invariant with respect to reparameterization and compatible with the Donoho-Huber breakdown point in linear regression situations. It also overcomes certain limitations of the definition proposed by Stromberg and Ruppert and can be used in a wide range of estimation problems. We investigate the breakdown properties of some nonlinear regression estimators. These results alert us to the danger of using familiar M estimators with data sets containing outliers and to the advantages of using estimators based on Hampel's proposal, such as S estimators.

Key Words:

• Badness measure
• High breakdown estimators
• Loss function
• Nonlinear regression
• M-estimators