## Abstract

We consider the exact and approximate computational complexity of the multivariate least median-of-squares (LMS) linear regression estimator. The LMS estimator is among the most widely used robust linear statistical estimators. Given a set of n points in ℝ^{d} and a parameter k, the problem is equivalent to computing the narrowest slab bounded by two parallel hyperplanes that contains k of the points. We present algorithms for the exact and approximate versions of the multivariate LMS problem. We also provide nearly matching lower bounds for these problems. These lower bounds hold under the assumptions that k is Ω(n) and that deciding whether n given points in ℝ^{d} are affinely non-degenerate requires Ω(n^{d}) time.

Original language | English (US) |
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Pages (from-to) | 593-607 |

Number of pages | 15 |

Journal | Discrete and Computational Geometry |

Volume | 36 |

Issue number | 4 |

DOIs | |

State | Published - Dec 2006 |

## ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics