Absolute approximation of Tukey depth: Theory and experiments

Authors:
Dan Chen;Pat Morin;Uli Wagner
Affiliations:
School of Computer Science, Carleton University, Ottawa, ON, K1S 5B6, Canada;School of Computer Science, Carleton University, Ottawa, ON, K1S 5B6, Canada;Institut für Theoretische Informatik, ETH Zürich, CH-8092 Zürich, Switzerland
Venue:
Computational Geometry: Theory and Applications
Year:
2013

Citing 10
Cited 0

Quasi-optimal range searching in spaces of finite VC-dimension

Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Dehn-Sommerville relations, upper bound theorem, and levels in arrangements

SCG '93 Proceedings of the ninth annual symposium on Computational geometry
The complexity and approximability of finding maximum feasible subsystems of linear relations

Theoretical Computer Science
Optimization in Arrangements

STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
On Spanning Trees with Low Crossing Numbers

Data Structures and Efficient Algorithms, Final Report on the DFG Special Joint Initiative
An optimal randomized algorithm for maximum Tukey depth

SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Low-Dimensional Linear Programming with Violations

SIAM Journal on Computing
On approximate range counting and depth

SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
The random Tukey depth

Computational Statistics & Data Analysis
Output-sensitive algorithms for Tukey depth and related problems

Statistics and Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

A Monte Carlo approximation algorithm for the Tukey depth problem in high dimensions is introduced. The algorithm is a generalization of an algorithm presented by Rousseeuw and Struyf (1998) [20]. The performance of this algorithm is studied both analytically and experimentally.