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

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  • Marc Ditzhaus
  • Daniel Gaigall

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.

Suggested Citation

  • Marc Ditzhaus & Daniel Gaigall, 2018. "A consistent goodness-of-fit test for huge dimensional and functional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 30(4), pages 834-859, October.
    • Handle: RePEc:taf:gnstxx:v:30:y:2018:i:4:p:834-859
    DOI: 10.1080/10485252.2018.1486402
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    Cited by:

    1. Norbert Henze & María Dolores Jiménez‐Gamero, 2021. "A test for Gaussianity in Hilbert spaces via the empirical characteristic functional," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 406-428, June.
    2. Marc Ditzhaus & Daniel Gaigall, 2022. "Testing marginal homogeneity in Hilbert spaces with applications to stock market returns," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 749-770, September.

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