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A consistent goodness-of-fit test for huge dimensional and functional data

  • A nonparametric goodness-of-fit test for random variables with values in a separable Hilbert space is investigated. To verify the null hypothesis that the data come from a specific distribution, an integral type test based on a Cramér-von-Mises statistic is suggested. The convergence in distribution of the test statistic under the null hypothesis is proved and the test's consistency is concluded. Moreover, properties under local alternatives are discussed. Applications are given for data of huge but finite dimension and for functional data in infinite dimensional spaces. A general approach enables the treatment of incomplete data. In simulation studies the test competes with alternative proposals.

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Author:Marc Ditzhaus, Daniel Gaigall
Parent Title (English):Journal of Nonparametric Statistics
Publisher:Taylor & Francis
Place of publication:Abingdon
Document Type:Article
Year of Completion:2018
Date of first Publication:2018/06/20
Date of the Publication (Server):2023/01/16
Tag:Cramér-von-Mises statistic; functional data; huge dimensional data; separable Hilbert space
First Page:834
Last Page:859
Institutes:FH Aachen / Fachbereich Medizintechnik und Technomathematik
collections:Verlag / Taylor & Francis