Minimum distance method for directional data and outlier detection
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.
KeywordsDirectional data Robust estimation Outlier detection Asymptotic properties
Mathematics Subject ClassificationPrimary 62F35 Secondary 62G05
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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