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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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