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Advances in Data Analysis and Classification

, Volume 12, Issue 3, pp 587–603 | Cite as

Minimum distance method for directional data and outlier detection

  • Mercedes Fernandez Sau
  • Daniela Rodriguez
Regular Article

Abstract

In this paper, we propose estimators based on the minimum distance for the unknown parameters of a parametric density on the unit sphere. We show that these estimators are consistent and asymptotically normally distributed. Also, we apply our proposal to develop a method that allows us to detect potential atypical values. The behavior under small samples of the proposed estimators is studied using Monte Carlo simulations. Two applications of our procedure are illustrated with real data sets.

Keywords

Directional data Robust estimation Outlier detection Asymptotic properties 

Mathematics Subject Classification

Primary 62F35 Secondary 62G05 

Notes

Acknowledgements

This work was done when the second author was visiting the Universität Regensburg, she is very grateful to the professors Rolf Tschernig and Stefan Rameseder for their kind hospitality. This research was partially supported by Grants 20020120200244BA from the Universidad de Buenos Aires, pip 11220110100742 from conicet and pict-2012-1641 from anpcyt, Argentina.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Ciclo Básico ComúnUniversidad de Buenos AiresBuenos AiresArgentina
  2. 2.Facultad de Ciencias Exactas y NaturalesUniversidad de Buenos AiresBuenos AiresArgentina
  3. 3.CONICETBuenos AiresArgentina

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