A universal deviation inequality for random polytopes

2013/11/12 by Victor-Emmanuel Brunel, Brunel, Victor-Emmanuel · 1 citation
Computer Science · Mathematics · #Computational Geometry and Mesh Generation #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Point processes and geometric inequalities #Statistics Theory (math.ST) #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1311.2902

arxiv created 2013/11/12 · openalex publication_date 2013/11/12 · arxiv updated 2013/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the convex hull of a finite sample of i.i.d. points uniformly distributed in a convex body in \R^d, d≥ 2. We prove an exponential deviation inequality, which leads to rate optimal upper bounds on all the moments of the missing volume of the convex hull, uniformly over all convex bodies of \R^d, with no restriction on their volume, location in the space and smoothness of the boundary.

Citations

• Adaptive estimation of convex and polytopal support

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• The wrapping hull and a unified framework for volume estimation

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