A consistent goodness-of-fit test for huge dimensional and functional data. Issue 4 (2nd October 2018)

• Record Type: Journal Article
• Authors: Ditzhaus, Marc; Gaigall, Daniel
• Is Part Of: Journal of nonparametric statistics. Volume 30:Issue 4(2018)
• Page Start: 834
• Page End: 859
• Publication Date: 2018-10-02
• Subjects: Cramér-von-Mises statistic -- separable Hilbert space -- huge dimensional data -- functional data; Nonparametric statistics -- Periodicals; 519.5
• DOI: 10.1080/10485252.2018.1486402
• Languages: English
• ISSNs: 1048-5252

Abstract

ABSTRACT: 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.