Quantile approximation for robust statistical estimation and k-enclosing problems

David M. Mount, Nathan S. Netanyahu, Christine D. Piatko, Ruth Silverman, Angela Y. Wu

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Given a set P of n points in Rd, a fundamental problem in computational geometry is concerned with finding the smallest shape of some type that encloses all the points of P. Well-known instances of this problem include finding the smallest enclosing box, minimum volume ball, and minimum volume annulus. In this paper we consider the following variant: Given a set of n points in Rd, find the smallest shape in question that contains at least k points or a certain quantile of the data. This type of problem is known as a k-enclosing problem. We present a simple algorithmic framework for computing quantile approximations for the minimum strip, ellipsoid, and annulus containing a given quantile of the points. The algorithms run in O(n log n) time.

Original languageEnglish
Pages (from-to)593-608
Number of pages16
JournalInternational Journal of Computational Geometry and Applications
Issue number6
StatePublished - Dec 2000


  • LMS regression
  • Minimum enclosing disk
  • Minimum volume ball/ellipsoid/annulus estimator
  • Robust estimation


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