Unbiased estimation of the volume of a convex body

Nikolay Baldin and Markus Reiß

Stochastic Processes and their Applications, 2016, vol. 126, issue 12, 3716-3732

Abstract: Based on observations of points uniformly distributed over a convex set in Rd, a new estimator for the volume of the convex set is proposed. The estimator is minimax optimal and also efficient non-asymptotically: it is nearly unbiased with minimal variance among all unbiased oracle-type estimators. Our approach is based on a Poisson point process model and as an ingredient, we prove that the convex hull is a sufficient and complete statistic. No hypotheses on the boundary of the convex set are imposed. In a numerical study, we show that the estimator outperforms earlier estimators for the volume. In addition, an adjusted set estimator for the convex body itself is proposed.

Keywords: Volume estimation; Convex hull; Poisson point process; UMVU; Stopping set; Exact oracle inequality; Missing volume (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2016.04.014

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