On the least median square problem

Research output: Contribution to conferencePaperpeer-review


We consider the exact and approximate computational complexity of the multivariate LMS linear regression estimator. The LMS estimator is among the most widely used robust linear statistical estimators. Given a set of n points in ℝd 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, under the assumption that deciding whether n given points in ℝd are affinely nondegenerate requires Ω(nd) time.

Original languageEnglish (US)
Number of pages7
StatePublished - 2004
EventProceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04) - Brooklyn, NY, United States
Duration: Jun 9 2004Jun 11 2004


OtherProceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04)
Country/TerritoryUnited States
CityBrooklyn, NY


  • Approximation algorithms
  • LMS regression
  • Lower bounds
  • Robust statistics

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Mathematics


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