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Limiting behavior of U-statistics, V-statistics, and one sample rank order statistics for nonstationary absolutely regular processes

Author

Listed:
  • Harel, Michel
  • Puri, Madan L.

Abstract

The weak convergences of U- and V-statistics were established by Yoshihara (1976, Z. Warsch. Verw. Gebiete 35 237-252) for stationary absolutely regular processes. Later Yoshihara (1978, Z. Warsch. Verw. Gebiete 43 101-127) also proved the weak convergence of one sample rank order statistics under similar conditions. In this paper, we extend some of Yoshihara's results to the nonstationary cases.

Suggested Citation

  • Harel, Michel & Puri, Madan L., 1989. "Limiting behavior of U-statistics, V-statistics, and one sample rank order statistics for nonstationary absolutely regular processes," Journal of Multivariate Analysis, Elsevier, vol. 30(2), pages 181-204, August.
    • Handle: RePEc:eee:jmvana:v:30:y:1989:i:2:p:181-204
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    Citations

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    Cited by:

    1. Joseph Ngatchou-Wandji & Michel Harel, 2013. "A Cramér-von Mises test for symmetry of the error distribution in asymptotically stationary stochastic models," Statistical Inference for Stochastic Processes, Springer, vol. 16(3), pages 207-236, October.
    2. Joseph Ngatchou-Wandji & Madan L. Puri & Michel Harel & Echarif Elharfaoui, 2019. "Testing nonstationary and absolutely regular nonlinear time series models," Statistical Inference for Stochastic Processes, Springer, vol. 22(3), pages 557-593, October.
    3. Joseph Ngatchou-Wandji & Echarif Elharfaoui & Michel Harel, 2022. "On change-points tests based on two-samples U-Statistics for weakly dependent observations," Statistical Papers, Springer, vol. 63(1), pages 287-316, February.

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