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Robust Statistical Engineering by Means of Scaled Bregman Distances

In: Recent Advances in Robust Statistics: Theory and Applications

Author

Listed:
  • Anna-Lena Kißlinger

    (University of Erlangen-Nürnberg, Chair of Statistics and Econometrics)

  • Wolfgang Stummer

    (University of Erlangen-Nürnberg, Department of Mathematics
    Affiliated Faculty Member of the School of Business and Economics, University of Erlangen-Nürnberg)

Abstract

We show how scaled Bregman distances can be used for the goal-oriented design of new outlier- and inlier robust statistical inference tools. Those extend several known distance-based robustness (respectively, stability) methods at once. Numerous special cases are illustrated, including 3D computer graphical comparison methods. For the discrete case, some universally applicable results on the asymptotics of the underlying scaled-Bregman-distance test statistics are derived as well.

Suggested Citation

  • Anna-Lena Kißlinger & Wolfgang Stummer, 2016. "Robust Statistical Engineering by Means of Scaled Bregman Distances," Springer Books, in: Claudio Agostinelli & Ayanendranath Basu & Peter Filzmoser & Diganta Mukherjee (ed.), Recent Advances in Robust Statistics: Theory and Applications, pages 81-113, Springer.
    • Handle: RePEc:spr:sprchp:978-81-322-3643-6_5
    DOI: 10.1007/978-81-322-3643-6_5
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