Computing projection depth and its associated estimators

Authors:
Xiaohui Liu;Yijun Zuo
Affiliations:
School of Statistics, Jiangxi University of Finance and Economics, Nanchang, China 330013 and Department of Statistics and Probability, Michigan State University, East Lansing, USA 48823;Department of Statistics and Probability, Michigan State University, East Lansing, USA 48823
Venue:
Statistics and Computing
Year:
2014

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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驴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.