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Limiting behavior of the perturbed empirical distribution functions evaluated at U -statistics for strongly mixing sequences of random variables

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  • Shan Sun
  • Ching-Yuan Chiang

Abstract

We prove the almost sure representation, a law of the iterated logarithm and an invariance principle for the statistic F ˆ n ( U n ) for a class of strongly mixing sequences of random variables { X i , i ≥ 1 } . Stationarity is not assumed. Here F ˆ n is the perturbed empirical distribution function and U n is a U -statistic based on X 1 , … , X n .

Suggested Citation

  • Shan Sun & Ching-Yuan Chiang, 1997. "Limiting behavior of the perturbed empirical distribution functions evaluated at U -statistics for strongly mixing sequences of random variables," International Journal of Stochastic Analysis, Hindawi, vol. 10, pages 1-18, January.
    • Handle: RePEc:hin:jnijsa:742120
    DOI: 10.1155/S1048953397000026
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    Cited by:

    1. Marie Hušková & Matúš Maciak, 2017. "Discontinuities in robust nonparametric regression with α-mixing dependence," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(2), pages 447-475, April.
    2. Francesco Bravo & Ba M. Chu & David T. Jacho-Chávez, 2017. "Semiparametric estimation of moment condition models with weakly dependent data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(1), pages 108-136, January.
    3. Xiaojun Song & Haoyu Wei, 2021. "Nonparametric Tests of Conditional Independence for Time Series," Papers 2110.04847, arXiv.org.

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