Advertisement

Statistics and Computing

, Volume 14, Issue 2, pp 91–98 | Cite as

Calculating the simplex median

  • Xin Huang
  • Christopher G. Small
Article
  • 135 Downloads

Abstract

While much attention has recently focussed on the use of multivariate medians for estimating the centre of a data set, a particular median based upon random simplexes proposed by Liu has been overshadowed by progress on other multivariate medians. The purpose of this paper is to redress the balance, and to show that Liu's simplex median is tractable, and has distinctive desirable properties that recommend it for use in data analysis.

simplex median multivariate data quasi-newton optimization 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aloupis G. 2001. On computing geometric estimators of location. M.Sc. Thesis, McGill University.Google Scholar
  2. Aloupis G., Cortés C., Gómez F., Soss M., and Toussaint G. 2001. Lower bounds for computing statistical depth. Technical Report SOCS-01.1, School of Computer Science, McGill University.Google Scholar
  3. Aloupis G., Langerman S., Soss M., and Toussaint G. 2002. Algorithms for bivariate medians and a Fermat-Torricelli problem for lines. Manuscript.Google Scholar
  4. Berg M.D., Kreveld M.V., Overmars M., and Schwarzkopf O. 1997. Computational Geometry: Algorithms and Applications. Springer-Verlag, Berlin, 170.Google Scholar
  5. Chaudhuri P. 1992. Multivariate location estimation using extension of R-estimates through U-statistics type approach. Ann. Statist. 20: 897–916.Google Scholar
  6. Liu R. 1990. On a notion of data depth based upon random simplices. Ann. Statist. 18: 405–414.Google Scholar
  7. O'Rourke J. 1994. Computational Geometry. C. Cambridge University Press, New York, 207.Google Scholar
  8. Rousseeuw P. and Ruts I. 1996. Bivariate location depth. Applied Statistics 45: 515–526.Google Scholar
  9. Small C.G. 1990. A survey of multidimensional medians. Int. Statist. Rev. 58: 263–277.Google Scholar
  10. Tukey J. 1975. Mathematics and the picturing of data. In Proc. Int. Congress of Mathematicians, Vancouver, pp. 523–531.Google Scholar
  11. Vardi Y. and Zhang C.-H. 2000. The multivariate L 1-median and associated data depth. Proc. Nat. Acad. Sc. 97: 1423–1426.Google Scholar
  12. Weiss M.A. 1993. Data Structures and Algorithm Analysis. C. Benjamin/Cummings, California, 217.Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Xin Huang
    • 1
  • Christopher G. Small
    • 1
  1. 1.University of WaterlooWaterlooCanada

Personalised recommendations