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Convergence of the empirical two-sample U-statistics with \(\beta\)-mixing data

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Abstract

We consider the empirical two-sample U-statistic with \(\beta\)-mixing strictly stationary data and investigate its convergence in Skorohod spaces. We then provide an application of such convergence.

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Acknowledgements

The authors would like to thank the referee for valuable comments that improved the quality of the paper.

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Authors and Affiliations

  1. Ruhr-Universität Bochum, 44780, Bochum, Germany

    H. Dehling & D. Giraudo

  2. Mirzo Ulugbek National University of Uzbekistan, Mathematical faculty, 4 University str., 100714, Tashkent, Uzbekistan

    O. Sharipov

Authors
  1. H. Dehling
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  2. D. Giraudo
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  3. O. Sharipov
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Corresponding author

Correspondence to D. Giraudo.

Additional information

This research was supported by the DFG Collaborative Research Center SFB 823 ‘Statistical modelling of nonlinear dynamic processes’.

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Dehling, H., Giraudo, D. & Sharipov, O. Convergence of the empirical two-sample U-statistics with \(\beta\)-mixing data. Acta Math. Hungar. 164, 377–412 (2021). https://doi.org/10.1007/s10474-021-01156-4

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  • DOI: https://doi.org/10.1007/s10474-021-01156-4

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