Uncertainty Assessment of Some Data-Adaptive M-Estimators

  • Jan Martin BrockmannEmail author
  • Boris Kargoll
Conference paper
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 137)


In this paper, we review a data-adaptive class of robust estimators consisting of convex combinations of the loss functions with respect to the L 1- and Huber’s M-estimator as proposed by Dodge and :̧def :̧def Jureckova (2000). The great advantage of this approach in comparison to the traditional procedure of applying a single estimator is that the optimal weight factor, representing the data-dependent minimum-variance estimator within that class, may be estimated from the data itself. Depending on the data characteristics, one could obtain pure L 2, L 1 and Huber’s estimator, as well as any convex combination between these three. We demonstrate the computational and statistical efficiency of this approach by providing an iteratively reweighted least squares algorithm and Monte Carlo uncertainties of the weight factor.



The computations were performed on the JUMP supercomputer in Jülich. The computing time was granted by the John von Neumann Institute for Computing (project 1827)


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Institute of Geodesy and Geoinformation, Department of Theoretical GeodesyUniversity of BonnBonnGermany

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