Confidence Sets for the Aumann Mean of a Random Closed Set

Seri, Raffaello; Choirat, Christine

doi:10.1007/978-3-540-24767-8_31

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“…We also study their variability using the concept of confidence regions. Seri and Choirat (2004) present two methods for the calculation of the confidence region of the Aumann expectation. To our best knowledge, this is the only other time confidence regions were studied in the context of random sets.…”

Section: Introductionmentioning

confidence: 99%

Confidence Regions for Means of Random Sets Using Oriented Distance Functions

Jankowski

Stanberry²

2012

Scandinavian J Statistics

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Image analysis frequently deals with shape estimation and image reconstruction. The objects of interest in these problems may be thought of as random sets, and one is interested in finding a representative, or expected, set. We consider a definition of set expectation using oriented distance functions and study the properties of the associated empirical set. Conditions are given such that the empirical average is consistent, and a method to calculate a confidence region for the expected set is introduced. The proposed method is applied to both real and simulated data examples.

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Section: Introductionmentioning

confidence: 99%