### 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.

Original language | English (US) |
---|---|

Pages (from-to) | 259-266 |

Number of pages | 8 |

Journal | Statistics and Computing |

Volume | 18 |

Issue number | 3 |

DOIs | |

State | Published - Sep 2008 |

### Fingerprint

### Keywords

- Algorithms
- Computational geometry
- Computational statistics
- Fixed-parameter tractability
- Halfspace depth
- Tukey depth

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computational Theory and Mathematics
- Statistics and Probability

### Cite this

*Statistics and Computing*,

*18*(3), 259-266. https://doi.org/10.1007/s11222-008-9054-2

**Output-sensitive algorithms for Tukey depth and related problems.** / Bremner, David; Chen, Dan; Iacono, John; Langerman, Stefan; Morin, Pat.

Research output: Contribution to journal › Article

*Statistics and Computing*, vol. 18, no. 3, pp. 259-266. https://doi.org/10.1007/s11222-008-9054-2

}

TY - JOUR

T1 - Output-sensitive algorithms for Tukey depth and related problems

AU - Bremner, David

AU - Chen, Dan

AU - Iacono, John

AU - Langerman, Stefan

AU - Morin, Pat

PY - 2008/9

Y1 - 2008/9

N2 - 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.

AB - 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.

KW - Algorithms

KW - Computational geometry

KW - Computational statistics

KW - Fixed-parameter tractability

KW - Halfspace depth

KW - Tukey depth

UR - http://www.scopus.com/inward/record.url?scp=45449089439&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=45449089439&partnerID=8YFLogxK

U2 - 10.1007/s11222-008-9054-2

DO - 10.1007/s11222-008-9054-2

M3 - Article

VL - 18

SP - 259

EP - 266

JO - Statistics and Computing

JF - Statistics and Computing

SN - 0960-3174

IS - 3

ER -