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

Marina T. Dietrich (), Dennis Dobler () and Mathisca C. M. Gunst
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Marina T. Dietrich: Vrije Universiteit Amsterdam
Dennis Dobler: Vrije Universiteit Amsterdam
Mathisca C. M. Gunst: Vrije Universiteit Amsterdam

Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, 2025, vol. 31, issue 3, No 6, 657 pages

Abstract: 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.

Keywords: Counting processes; Martingale theory; Resampling; Statistical inference; Survival analysis; Wild bootstrap (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10985-025-09659-w

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