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Functional limit theorems for U-statistics in the degenerate case

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  • Neuhaus, Georg

Abstract

[9] established multidimensional functional limit theorems for generalized U-statistics for estimable parameters which are stationary of order zero (the nondegenerate case). Similar univariate and bivariate functional limit theorems are derived for U-statistics in the degenerate case. The latter are close connected with one- or two-sample Cramér-von Mises statistics.

Suggested Citation

  • Neuhaus, Georg, 1977. "Functional limit theorems for U-statistics in the degenerate case," Journal of Multivariate Analysis, Elsevier, vol. 7(3), pages 424-439, September.
    • Handle: RePEc:eee:jmvana:v:7:y:1977:i:3:p:424-439
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    Cited by:

    1. Xu Li & Wenjuan Hu & Baoxue Zhang, 2023. "Measuring and testing homogeneity of distributions by characteristic distance," Statistical Papers, Springer, vol. 64(2), pages 529-556, April.
    2. Alba Fernández, V. & Jiménez Gamero, M.D. & Muñoz Garcia, J., 2008. "A test for the two-sample problem based on empirical characteristic functions," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3730-3748, March.
    3. Holzmann, Hajo & Koch, Susanne & Min, Aleksey, 2004. "Almost sure limit theorems for U-statistics," Statistics & Probability Letters, Elsevier, vol. 69(3), pages 261-269, September.
    4. M. Ahmad, 2014. "A $$U$$ -statistic approach for a high-dimensional two-sample mean testing problem under non-normality and Behrens–Fisher setting," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(1), pages 33-61, February.
    5. Marie Hušková & Simos Meintanis, 2008. "Tests for the multivariate -sample problem based on the empirical characteristic function," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(3), pages 263-277.
    6. Cabus, Patricia & Guillotin-Plantard, Nadine, 2002. "Functional limit theorems for U-statistics indexed by a random walk," Stochastic Processes and their Applications, Elsevier, vol. 101(1), pages 143-160, September.

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