Given a set of n points in the plane, a method is described for constructing a nested sequence of m < n/2 convex polygons based on the points. If the points are a random sample, it is shown that the convex sets share some of the distributional properties of one-dimensional order statistics. An algorithm which requires 0(n3) time and 0(n2) space is described for constructing the sequence of convex sets.

Key words

convex polygon order statistic intersection 


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  1. Barnett, V. (1976). The ordering of multivariate data. J. R. Statis. Soc. A, 139, 318–354.Google Scholar
  2. Bebbington, A. C. (1978). A method of bivariate trimming for robust estimation of the correlation coefficient. Appl. Statist. 27, 221–226.Google Scholar
  3. Blum, M., R. W. Floyd, V. R. Pratt, R. L. Rivest and R. E. Tarjan (1972). Time bounds for selection. J. Computer and System Sciences, 7, 448–461.MathSciNetCrossRefGoogle Scholar
  4. David, H. A. (1970). Order Statistics, Wiley, New York.zbMATHGoogle Scholar
  5. Eddy, W. F. (1977). A new convex hull algorithm for planar sets. ACM Trans. Math. Software, 3, 398–403.Google Scholar
  6. Eddy, W. F. (1980). The distribution of the convex hull of a Gaussian sample. J. Appl. Prob., 17, 686–695.Google Scholar
  7. Eddy, W. F. (1981). Discussion of “Graphics for the Multivariate Two Sample Problem” by J. H. Friedman and L. C. Rafsky, J. Amer. Statist. Assoc., 76, 287–289.Google Scholar
  8. Eddy, W. F. and J. D. Gale (1981). The convex hull of a spherically symmetric sample. Adv. Appl. Prob., 13, 751–763.Google Scholar
  9. Graham, R. L. (1972). An efficient algorithm for determining the convex hull of a planar set. Inform. Proc. Letters, 1, 132–133.Google Scholar
  10. Green, P. J. (1980). Peeling bivariate data. Proc. Sheffield Conf. Multivariate Data Analysis, Chapter 1, 3–19.Google Scholar
  11. Huber, P. J. (1972). Robust statistics: A review. Ann. Math. Statist., 43, 1041–1067.MathSciNetzbMATHCrossRefGoogle Scholar
  12. Matheron, G. (1975). Random Sets and Integral Geometry, Wiley, New York.Google Scholar
  13. Tukey, J. W. (1975). Mathematics and the picturing of data. Proc. Int. Cong. Math., Vancouver, 1974, Vol. 2, 523–531.Google Scholar

Copyright information

© Physica-Verlag, Vienna for IASC (International Association for Statistical Computing) 1982

Authors and Affiliations

  • W. F. Eddy
    • 1
  1. 1.Carnegie-Mellon UniversityPittsburghUSA

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