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On functionals of random convex hulls
Author(s) -
Small Christopher G.
Publication year - 1989
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3314761
Subject(s) - convex hull , mathematics , combinatorics , centroid , regular polygon , dimension (graph theory) , convex set , subderivative , geometry , convex optimization
The completeness of the induced distribution of the convex hull of a random set of points drawn uniformly from a convex region seems not to have been noticed before. The result generalizes a well‐known result for dimension one. As a consequence, there exists a theory of best unbiased estimation for certain functionals of the convex region. For example, a best estimator of the centroid of the convex region can be constructed. This estimator is distinct from the centroid of the convex hull. Therefore another generalization of a property holding in dimension one, namely the unbiased‐ness of the centroid of the convex hull, is seen to fail.