Lower bounds for computing statistical depth

Greg Aloupis, Carmen Cortés, Francisco Gómez, Michael Soss, Godfried Toussaint

Research output: Contribution to journalArticle

Abstract

Given a finite set of points S, two measures of the depth of a query point χ with respect to S are the Simplicial depth of Liu and the Halfspace depth of Tukey (also known as Location depth). We show that computing these depths requires Ω(n log n) time, which matches the upper bound complexities of the algorithms of Rousseeuw and Ruts. Our lower bound proofs may also be applied to two bivariate sign tests: that of Hodges, and that of Oja and Nyblom.

Original languageEnglish (US)
Pages (from-to)223-229
Number of pages7
JournalComputational Statistics and Data Analysis
Volume40
Issue number2
DOIs
StatePublished - Aug 28 2002

Fingerprint

Statistical Computing
Lower bound
Halfspace Depth
Sign Test
Set of points
Finite Set
Query
Upper bound
Computing

Keywords

  • Halfspace depth
  • Liu
  • Sign tests
  • Simplical depth
  • Tukey

ASJC Scopus subject areas

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

Cite this

Lower bounds for computing statistical depth. / Aloupis, Greg; Cortés, Carmen; Gómez, Francisco; Soss, Michael; Toussaint, Godfried.

In: Computational Statistics and Data Analysis, Vol. 40, No. 2, 28.08.2002, p. 223-229.

Research output: Contribution to journalArticle

Aloupis, Greg ; Cortés, Carmen ; Gómez, Francisco ; Soss, Michael ; Toussaint, Godfried. / Lower bounds for computing statistical depth. In: Computational Statistics and Data Analysis. 2002 ; Vol. 40, No. 2. pp. 223-229.
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