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Limit theorems for permutations of empirical processes with applications to change point analysis

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  • Horváth, Lajos
  • Shao, Qi-Man

Abstract

Theorems of approximation of Gaussian processes for the sequential empirical process of the permutations of independent random variables are established. The results are applied to simulate critical values for the functionals of sequential empirical processes used in change point analysis. The proofs are based on the properties of rank statistics and negatively associated random variables.

Suggested Citation

  • Horváth, Lajos & Shao, Qi-Man, 2007. "Limit theorems for permutations of empirical processes with applications to change point analysis," Stochastic Processes and their Applications, Elsevier, vol. 117(12), pages 1870-1888, December.
    • Handle: RePEc:eee:spapps:v:117:y:2007:i:12:p:1870-1888
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    References listed on IDEAS

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    1. Husková, M., 1997. "Limit theorems for rank statistics," Statistics & Probability Letters, Elsevier, vol. 32(1), pages 45-55, February.
    2. Duembgen, Lutz, 1998. "Symmetrization and decoupling of combinatorial random elements," Statistics & Probability Letters, Elsevier, vol. 39(4), pages 355-361, August.
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    Cited by:

    1. Bücher, Axel & Ruppert, Martin, 2013. "Consistent testing for a constant copula under strong mixing based on the tapered block multiplier technique," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 208-229.
    2. Holmes, Mark & Kojadinovic, Ivan & Quessy, Jean-François, 2013. "Nonparametric tests for change-point detection à la Gombay and Horváth," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 16-32.

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