## Median hyperplanes in normed spaces

- In this paper we deal with the location of hyperplanes in n-dimensional normed spaces. If d is a distance measure, our objective is to find a hyperplane H which minimizes f(H) = sum_{m=1}^{M} w_{m}d(x_m,H), where w_m ge 0 are non-negative weights, x_m in R^n, m=1, ... ,M demand points and d(x_m,H)=min_{z in H} d(x_m,z) is the distance from x_m to the hyperplane H. In robust statistics and operations research such an optimal hyperplane is called a median hyperplane. We show that for all distance measures d derived from norms, one of the hyperplanes minimizing f(H) is the affine hull of n of the demand points and, moreover, that each median hyperplane is (ina certain sense) a halving one with respect to the given point set.

Author: | Anita Schöbel, H. Martini |
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URN (permanent link): | urn:nbn:de:hbz:386-kluedo-4590 |

Serie (Series number): | Report in Wirtschaftsmathematik (WIMA Report) (18) |

Document Type: | Preprint |

Language of publication: | English |

Year of Completion: | 1999 |

Year of Publication: | 1999 |

Publishing Institute: | Technische Universität Kaiserslautern |

Date of the Publication (Server): | 2000/04/03 |

Faculties / Organisational entities: | Fachbereich Mathematik |

DDC-Cassification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |

Licence (German): | Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011 |