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Change-point detection and bootstrap for Hilbert space valued random fields

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  • Bucchia, Béatrice
  • Wendler, Martin

Abstract

The problem of testing for the presence of epidemic changes in random fields is investigated. In order to be able to deal with general changes in the marginal distribution, a Cramér–von Mises type test is introduced which is based on Hilbert space theory. A functional central limit theorem for ρ-mixing Hilbert space valued random fields is proven. In order to avoid the estimation of the long-run variance and obtain critical values, Shao’s dependent wild bootstrap method is adapted to this context. For this, a joint functional central limit theorem for the original and the bootstrap sample is shown. Finally, the theoretic results are supplemented by a short simulation study.

Suggested Citation

  • Bucchia, Béatrice & Wendler, Martin, 2017. "Change-point detection and bootstrap for Hilbert space valued random fields," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 344-368.
    • Handle: RePEc:eee:jmvana:v:155:y:2017:i:c:p:344-368
    DOI: 10.1016/j.jmva.2017.01.007
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    Cited by:

    1. Lea Wegner & Martin Wendler, 2024. "Robust change-point detection for functional time series based on U-statistics and dependent wild bootstrap," Statistical Papers, Springer, vol. 65(7), pages 4767-4810, September.
    2. Stoehr, Christina & Aston, John A D & Kirch, Claudia, 2021. "Detecting changes in the covariance structure of functional time series with application to fMRI data," Econometrics and Statistics, Elsevier, vol. 18(C), pages 44-62.
    3. Rice, Gregory & Zhang, Chi, 2022. "Consistency of binary segmentation for multiple change-point estimation with functional data," Statistics & Probability Letters, Elsevier, vol. 180(C).
    4. Muhammad Rizwan Khan & Biswajit Sarkar, 2019. "Change Point Detection for Airborne Particulate Matter ( PM 2.5 , PM 10 ) by Using the Bayesian Approach," Mathematics, MDPI, vol. 7(5), pages 1-42, May.
    5. Holger Dette & Kevin Kokot & Stanislav Volgushev, 2020. "Testing relevant hypotheses in functional time series via self‐normalization," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(3), pages 629-660, July.

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