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Wild bootstrap for counting process-based statistics: a martingale theory-based approach

Author

Listed:
  • Marina T. Dietrich

    (Vrije Universiteit Amsterdam
    University Augsburg)

  • Dennis Dobler

    (Vrije Universiteit Amsterdam
    TU Dortmund University
    University Alliance Ruhr)

  • Mathisca C. M. Gunst

    (Vrije Universiteit Amsterdam)

Abstract

The wild bootstrap is a popular resampling method in the context of time-to-event data analysis. Previous works established the large sample properties of it for applications to different estimators and test statistics. It can be used to justify the accuracy of inference procedures such as hypothesis tests or time-simultaneous confidence bands. This paper provides a general framework for establishing large sample properties in a unified way by using martingale structures. This framework includes most of the well-known parametric, semiparametric and nonparametric statistical methods in time-to-event analysis. Along the way of proving the validity of the wild bootstrap, a new variant of Rebolledo’s martingale central limit theorem for counting process-based martingales is developed as well.

Suggested Citation

  • Marina T. Dietrich & Dennis Dobler & Mathisca C. M. Gunst, 2025. "Wild bootstrap for counting process-based statistics: a martingale theory-based approach," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 31(3), pages 631-657, July.
    • Handle: RePEc:spr:lifeda:v:31:y:2025:i:3:d:10.1007_s10985-025-09659-w
    DOI: 10.1007/s10985-025-09659-w
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    References listed on IDEAS

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    1. D. Y. Lin & L. J. Wei & I. Yang & Z. Ying, 2000. "Semiparametric regression for the mean and rate functions of recurrent events," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 711-730.
    2. Ditzhaus, Marc & Pauly, Markus, 2019. "Wild bootstrap logrank tests with broader power functions for testing superiority," Computational Statistics & Data Analysis, Elsevier, vol. 136(C), pages 1-11.
    3. Dennis Dobler & Markus Pauly & ThomasH. Scheike, 2019. "Confidence bands for multiplicative hazards models: Flexible resampling approaches," Biometrics, The International Biometric Society, vol. 75(3), pages 906-916, September.
    4. D. Dobler & J. Beyersmann & M. Pauly, 2017. "Non-strange weird resampling for complex survival data," Biometrika, Biometrika Trust, vol. 104(3), pages 699-711.
    5. M Hiabu & J P Nielsen & T H Scheike, 2021. "Nonsmooth backfitting for the excess risk additive regression model with two survival time scales [A linear regression model for the analysis of life times]," Biometrika, Biometrika Trust, vol. 108(2), pages 491-506.
    6. Giorgos Bakoyannis, 2021. "Nonparametric analysis of nonhomogeneous multistate processes with clustered observations," Biometrics, The International Biometric Society, vol. 77(2), pages 533-546, June.
    7. Tobias Bluhmki & Dennis Dobler & Jan Beyersmann & Markus Pauly, 2019. "The wild bootstrap for multivariate Nelson–Aalen estimators," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(1), pages 97-127, January.
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