Regression Depth and Center Points

Details Regression Depth and Center Points Regression Depth and Center Points

1998-09-21

arxiv.org/abs/cs/9809037v2

Discrete Comput. Geom. 23(3):305-323, 2000

Computer Science

Computational Geometry

14 pages, 3 figures

Scientific paper

10.1007/PL00009502

We show that, for any set of n points in d dimensions, there exists a hyperplane with regression depth at least ceiling(n/(d+1)). as had been conjectured by Rousseeuw and Hubert. Dually, for any arrangement of n hyperplanes in d dimensions there exists a point that cannot escape to infinity without crossing at least ceiling(n/(d+1)) hyperplanes. We also apply our approach to related questions on the existence of partitions of the data into subsets such that a common plane has nonzero regression depth in each subset, and to the computational complexity of regression depth problems.

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