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Localized Cumulative Distributions and a Multivariate Generalization of the Cramér-von Mises Distance

Hanebeck, Uwe D.; Klumpp, Vesa

Abstract: This paper is concerned with distances for comparing multivariate random vectors with a special focus on the case that at least one of the random vectors is of discrete type, i.e., assumes values from a discrete set only. The first contribution is a new type of characterization of multivariate random quantities, the so called Localized Cumulative Distribution (LCD) that, in contrast to the conventional definition of a cumulative distribution, is unique and symmetric. Based on the LCDs of the random vectors under consideration, the second contribution is the definition of generalized distance measures that are suitable for the multivariate case. These distances are used for both analysis and synthesis purposes. Analysis is concerned with assessing whether a given sample stems from a given continuous distribution. Synthesis is concerned with both density estimation, i.e., calculating a suitable continuous approximation of a given sample, and density discretization, i.e., approximation of a given continuous random vector by a discrete one.

Zugehörige Institution(en) am KIT Institut für Anthropomatik (IFA)
Publikationstyp Proceedingsbeitrag
Jahr 2008
Sprache Englisch
Identifikator ISBN: 978-1-4244-2144-2
URN: urn:nbn:de:swb:90-348471
KITopen ID: 1000034847
Erschienen in Proceedings of the 2008 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2008), Seoul, Republic of Korea, August, 2008
Verlag IEEE, Piscataway
Seiten 33-39
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