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Journal of Applied Geodesy

Editor-in-Chief: Kahmen, Heribert / Rizos, Chris

CiteScore 2018: 1.61

SCImago Journal Rank (SJR) 2018: 0.532
Source Normalized Impact per Paper (SNIP) 2018: 1.064

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Volume 7, Issue 3


Expectation maximization algorithm for the variance-inflation model by applying the t-distribution

Karl-Rudolf Koch
  • Corresponding author
  • Institute of Geodesy and Geoinformation, Theoretical Geodesy, University of Bonn, Nussallee 17, 53115 Bonn, Germany
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/ Boris Kargoll
Published Online: 2013-08-06 | DOI: https://doi.org/10.1515/jag-2013-0007


An adaptive robust estimation for the linear model using the t-distribution is available. Unknown weights for the observations to identify outliers are introduced, i.e. the variance-inflation model is applied. The EM (expectation maximization) algorithm is used for the estimation of the unknown parameters and results in an iteratively reweighted least squares adjustment. Small weights indicate the outliers. However, it is found out here that the weights continuously increase for outliers with small absolute values without a hint where the outliers stop and the observations begin. The suspected outliers are therefore introduced into the EM algorithm for a robust estimation based on the mean-shift model. It starts with zero weights for the outliers and shows at the end of the iterations a clear indication between the weights for the outliers and the observations. Thus, the EM algorithms for the variance-inflation and the mean-shift model complement each other. The first algorithm is very sensitive to outliers because of its adaptive estimation and the second one provides the distinction between outliers and observations.

Keywords: Robust estimation; heavy-tailed distribution; mean-shift and variance-inflation model; gamma and loggamma distribution; psi (digamma) function; B-spline surface

About the article

Published Online: 2013-08-06

Published in Print: 2013-08-01

Citation Information: Journal of Applied Geodesy, Volume 7, Issue 3, Pages 217–225, ISSN (Online) 1862-9024, ISSN (Print) 1862-9016, DOI: https://doi.org/10.1515/jag-2013-0007.

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