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SS 2015
21.04.2015 um 12:00 Uhr in Raum 69/E15
Prof. Dr. Alexander Koldobsky (University of Missouri)
Slicing Inequalitites for Measures of Convex Bodies
28.04.2015 um 12:00 Uhr in Raum 69/E15
Benjamin Reichenwallner (Universität Salzburg, z.Zt. Universität Osnabrück)
Monotonicity of Random Polytopes
05.05.2015 um 12:00 Uhr in Raum 69/E15
Denise Günther (Universität Osnabrück)
Short Rate Modelle in der LVM
06.05.2015 um 13:00 Uhr in Raum 69/E18
Nicolas Chenavier (Université de Littoral)
A general study of extremes for a stationary random tessellation with a finite range condition
12.05.2015 um 12:00 Uhr in Raum 69/E15
Nikolay Baldin M. Sc. (Humboldt Universität zu Berlin)
Unbiased Estimation of the Volume of a Convex Body
Abstract: Based on observations of points uniformly distributed over a convex set in R^d, a new estimator for the volume of the convex set is constructed. 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 improved set estimator for the convex body itself is proposed.
