Abstract
The article describes and studies two methods of statistical estimation of various geometrical characteristics of convex compact random subsets in the Euclidean space. Estimation accuracy using a finite number of measurements is considered. A theorem characterizing Gaussian random sets is given, which states that all these sets are of the form A=M+ξ, where M has a degenerate distribution and ξ is a normal random vector.
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Literature cited
N. N. Lyashenko, “On limit theorems for sums of independent compact random subsets in the Euclidean space,” Zap. Nauch. Sem. Leningr. Otd. Mat. Inst.,85, 113–128 (1979).
R. T. Rockafellar, Convex Analysis, Princeton Univ. Press (1970).
J. Materon, Random Sets and Integral Geometry [Russian translation], Mir, Moscow (1978).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 98, pp. 115–139, 1980.
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Lyashenko, N.N. Statistics of random compacts in euclidean space. J Math Sci 21, 76–92 (1983). https://doi.org/10.1007/BF01091458
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DOI: https://doi.org/10.1007/BF01091458