Abstract
To facilitate the application of projection depth, an exact algorithm is proposed from the view of cutting a convex polytope with hyperplanes. Based on this algorithm, one can obtain a finite number of optimal direction vectors, which are x-free and therefore enable us (Liu et al., Preprint, 2011) to compute the projection depth and most of its associated estimators of dimension p≥2, including Stahel-Donoho location and scatter estimators, projection trimmed mean, projection depth contours and median, etc. Both real and simulated examples are also provided to illustrate the performance of the proposed algorithm.
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Acknowledgements
This work was done during Xiaohui Liu’s visit to the Department of Statistics and Probability at Michigan State University as a joint PhD student. He thanks his co-advisor Professor Yijun Zuo for stimulating discussions and insightful comments and suggestions and the department for providing excellent studying and working condition. The authors would like to thank two anonymous referees, an associate editor and the editor for their careful reading of the first version of this paper. Their constructive comments led to substantial improvements to the manuscript.
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Liu, X., Zuo, Y. Computing projection depth and its associated estimators. Stat Comput 24, 51–63 (2014). https://doi.org/10.1007/s11222-012-9352-6
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DOI: https://doi.org/10.1007/s11222-012-9352-6