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Exchangeably Weighted Bootstraps of General Markov U -Process

Author

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  • Inass Soukarieh

    (Laboratory of Applied Mathematics of Compiègne (LMAC), Université de Technologie de Compiègne, 60200 Compiègne, France
    These authors contributed equally to this work.)

  • Salim Bouzebda

    (Laboratory of Applied Mathematics of Compiègne (LMAC), Université de Technologie de Compiègne, 60200 Compiègne, France
    These authors contributed equally to this work.)

Abstract

We explore an exchangeably weighted bootstrap of the general function-indexed empirical U -processes in the Markov setting, which is a natural higher-order generalization of the weighted bootstrap empirical processes. As a result of our findings, a considerable variety of bootstrap resampling strategies arise. This paper aims to provide theoretical justifications for the exchangeably weighted bootstrap consistency in the Markov setup. General structural conditions on the classes of functions (possibly unbounded) and the underlying distributions are required to establish our results. This paper provides the first general theoretical study of the bootstrap of the empirical U -processes in the Markov setting. Potential applications include the symmetry test, Kendall’s tau and the test of independence.

Suggested Citation

  • Inass Soukarieh & Salim Bouzebda, 2022. "Exchangeably Weighted Bootstraps of General Markov U -Process," Mathematics, MDPI, vol. 10(20), pages 1-42, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3745-:d:939689
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    References listed on IDEAS

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    Cited by:

    1. Salim Bouzebda & Amel Nezzal & Tarek Zari, 2022. "Uniform Consistency for Functional Conditional U -Statistics Using Delta-Sequences," Mathematics, MDPI, vol. 11(1), pages 1-39, December.
    2. Salim Bouzebda, 2023. "On Weak Convergence of the Bootstrap Copula Empirical Process with Random Resample Size," Stats, MDPI, vol. 6(1), pages 1-16, February.
    3. Salim Bouzebda & Inass Soukarieh, 2022. "Non-Parametric Conditional U -Processes for Locally Stationary Functional Random Fields under Stochastic Sampling Design," Mathematics, MDPI, vol. 11(1), pages 1-69, December.
    4. Soukarieh, Inass & Bouzebda, Salim, 2023. "Renewal type bootstrap for increasing degree U-process of a Markov chain," Journal of Multivariate Analysis, Elsevier, vol. 195(C).
    5. Irene Votsi & Salim Bouzebda, 2025. "Bootstrap of Reliability Indicators for Semi-Markov Processes," Methodology and Computing in Applied Probability, Springer, vol. 27(1), pages 1-18, March.

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