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

Marina T Dietrich1,2, Dennis Dobler3,4,5, Mathisca C M de Gunst3

  • 1Department of Mathematics, Vrije Universiteit Amsterdam, 1081 HV, Amsterdam, The Netherlands. marina.dietrich@uni-a.de.

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Summary
This summary is machine-generated.

The wild bootstrap method is validated for time-to-event data analysis using martingale structures. This approach unifies statistical methods and proves the accuracy of inference procedures like hypothesis tests.

Keywords:
Counting processesMartingale theoryResamplingStatistical inferenceSurvival analysisWild bootstrap

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Area of Science:

  • Statistics
  • Survival Analysis
  • Resampling Methods

Background:

  • The wild bootstrap is a widely used resampling technique for time-to-event data.
  • Its large sample properties have been established for various estimators and test statistics.
  • It supports inference procedures like hypothesis tests and time-simultaneous confidence bands.

Purpose of the Study:

  • To present a general, unified framework for establishing large sample properties of the wild bootstrap.
  • To demonstrate the framework's applicability to a broad range of statistical methods in time-to-event analysis.
  • To introduce a novel variant of Rebolledo's martingale central limit theorem.

Main Methods:

  • Utilizing martingale structures to establish large sample properties.
  • Applying the framework to parametric, semiparametric, and nonparametric statistical methods.
  • Developing a new martingale central limit theorem for counting processes.

Main Results:

  • A unified framework for validating the wild bootstrap in time-to-event analysis is established.
  • The framework encompasses most common statistical methods in the field.
  • A new variant of the martingale central limit theorem is derived.

Conclusions:

  • The proposed martingale-based framework provides a robust and unified approach to justifying the wild bootstrap.
  • This work extends the theoretical underpinnings of resampling methods in survival analysis.
  • The newly developed martingale theorem contributes to the statistical theory for counting processes.