Abstract
AbstractConsider the random polytope that is given by the convex hull of a Poisson point process on a smooth convex body in $$\mathbb {R}^d$$
R
d
. We prove central limit theorems for continuous motion invariant valuations including the Wills functional and the intrinsic volumes of this random polytope. Additionally we derive a central limit theorem for the oracle estimator that is an unbiased and minimal variance estimator for the volume of a convex set. Finally we obtain a multivariate limit theorem for the intrinsic volumes and the components of the $$\mathbf {f}$$
f
-vector of the random polytope.
Publisher
Springer Science and Business Media LLC
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Cited by
1 articles.
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