Reliability Analysis for a Robust M-Estimator

Abstract

The least-squares estimation exhibits a poor performance in the presence of gross errors. One of the typical approaches to control the influence of outliers is to use robust estimation techniques. The well-established geodetic reliability theory is comprised of two main components: internal and external reliability. Both reliability measures are important diagnostic tools for inferring the strength of the model validation. To gain further insight into robust M-estimation performance, the variation characteristics of internal and external reliability measures are addressed for a particular robust estimator. Theoretical analyses show that, during the iterative reweighting procedure for uncorrelated observations, the internal reliability measures as represented by minimal detectable bias become larger and larger. For purpose of illustration, a numerical example associated with a simulated geodetic leveling network is provided. As expected, for the outlying observations, their corresponding external reliability measures get smaller and smaller when the iteratively reweighted least-squares method is implemented.