Output-sensitive algorithms for Tukey depth and related problems

Authors:
David Bremner;Dan Chen;John Iacono;Stefan Langerman;Pat Morin
Affiliations:
University of New Brunswick, New Brunswick, Canada;Carleton University, Ottawa, Canada;Polytechnic University, Brooklyn, USA;Université Libre de Bruxelles, Brussels, Belgium;School of Computer Science, Carleton University, Ottawa, Canada K1S 5B6
Venue:
Statistics and Computing
Year:
2008

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Abstract

The Tukey depth (Proceedings of the International Congress of Mathematicians, vol. 2, pp. 523---531, 1975) of a point p with respect to a finite set S of points is the minimum number of elements of S contained in any closed halfspace that contains p. Algorithms for computing the Tukey depth of a point in various dimensions are considered. The running times of these algorithms depend on the value of the output, making them suited to situations, such as outlier removal, where the value of the output is typically small.