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Original Articles

Maximum likelihood estimation in convex hull models

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Pages 3759-3777 | Received 01 Sep 1989, Published online: 27 Jun 2007

References

  • Artstein , Z. and Hart , S. 1981 . Law of Large Numbers for Random Sets and Allocation Processes . Math. Oper. REs , 6 : 485 – 492 .
  • Artstein , Z. and Vitale , R.A. 1975 . A Strong Law of Large Numbers for Random Compact Sets . Annals of Probability , 3 : 879 – 882 .
  • Carnal , H. 1970 . Die Konvexe Hulle von a rotationssymmetrisch verteilten Punkten . Z. Wahr verw. Gebiete , 15 : 168 – 176 .
  • Cressie , N. 1978 . A Strong Limit Theorem for Random Sets . Suppl. Adv. Appl. Probab , 10 : 36 – 46 .
  • Cressie , N. 1979 . A Central Limit Theorem for Random Sets . Z. Wahr. Verw. Gebiete , 49 : 37 – 47 .
  • Eddy , W.F. 1980 . The Distribution of the Convex Hull of a Gaussian Sample . Journal of Applied Probability , 17 : 686 – 695 .
  • Eddy , W.F. and Gale , J.D. 1981 . The Convex Hull of a Spherically Symmetric Sample . Advances in Probability , 13 : 751 – 763 .
  • Efron , Bradley . 1965 . The Convex Hull of a Random Set of Points . Biometrika , 52 : 331 – 343 .
  • Gale , J.D. 1980 . The Asymptotic Distribution of the Convex Hull of a Random Sample , Carnegie-Mellon University . unpublished Ph.D. Thesis Department of Statistics
  • Gine , E. , Hahn , M. and Zinn , J. . Limit Theorems for Random Sets: An application of probability in Banach space results . Proc. Fourth Int. Conf. on Probability in Banach spaces . Oberwolfach .
  • Jow , Richard L. 1983 . “ Some Contributions to the Theory of Random Sets ” . In Ph.D. thesis , Claremont Graduate School . unpublished Graduate Faculty of Mathematics
  • Lee , T.L. , Chen , K.W. and Attele , R. 1989 . “ Modelling Random Convex Sets ” . In 0 , Charlotte : University of North Carolina . Technical Report
  • Lyashenko , N.N. 1982 . Limit Theorems for Sums of Independent, Compact, Random Subsets of Euclidean space . J. Soviet Math , 20 : 2187 – 2296 . English translation
  • Lyashenko , N.N. 1983 . Statistics of Random Compacts in Euclidean space . J. Soviet Math , 21 : 76 – 92 . English translation
  • Mase , S. 1979 . Random Compact Convex Sets which are infinitely divisible with respect to Minkowski addition . Adv. Appl. Prob , 11 : 834 – 850 .
  • Puri , M.L. and Ralescu , D. 1983 . Strong Law of Large Numbers for Banach space valued Random Sets . Annals of Probability , 11 : 222 – 224 .
  • Puri , M.L. and Ralescu , D. 1985 . Limit Theorems for Random Convex Sets in Banach space . Math. Proc. Cambridge Phil. Soc , 97 : 151 – 158 .
  • Renyi , A. and Sulanke , R. 1964 . Uber die konvexe Hulle von a zufallig gewahlten Punkten . I and II, Z. Wahrscheinlichkeitsth , 2 : 75 – 84 . 3, 138-147
  • Trader , D.A. 1981 . “ Infinitely Divisible Random Sets ” . In unpublished Ph.D. Thesis , Carnegie-Mellon University . Department of Statistics
  • Trader , D.A. and Eddy , W.F. 1982 . Probability Functionals for Random Sets , Carnegie-Mellon University . Technical Report No. 252, Department of Statistics
  • Vitale , R.A. 1977 . Asymptotic Area and Perimeter of Sums of Random Plane Convex Sets , Vol. 1770 , University of Wisconsin-Madison Mathematics Research Center . Technical Summary Report
  • Vitale , R.A. 1983 . Some Developments in the Theory of Random Sets . Bull. Int. Statist. Inst , 50 : 863 – 871 .

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