Exactly computing bivariate projection depth contours and median

Authors:
Xiaohui Liu;Yijun Zuo;Zhizhong Wang
Affiliations:
School of Statistics, Jiangxi University of Finance and Economics, Nanchang, Jiangxi 330013, China and Department of Statistics and Probability, Michigan State University, East Lansing, MI 48823, ...;Department of Statistics and Probability, Michigan State University, East Lansing, MI 48823, USA;School of Mathematics Science and Computing Technology, Central South University, Hunan 410083, China
Venue:
Computational Statistics & Data Analysis
Year:
2013

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Abstract

Among their competitors, projection depth and its induced estimators are very favorable because they can enjoy very high breakdown point robustness without having to pay the price of low efficiency, meanwhile providing a promising center-outward ordering of multi-dimensional data. However, their further applications have been severely hindered due to their computational challenge in practice. In this paper, we derive a simple form of the projection depth function, when (@m,@s)= (Med, MAD). This simple form enables us to extend the existing result of point-wise exact computation of projection depth (PD) of Zuo and Lai (2011) to depth contours and median for bivariate data.