Canadian Journal of Statistics

On functionals of random convex hulls

Journal Article

Abstract

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.

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