2014/01/30 by Dennis Dobler, Markus Pauly, Dobler, Dennis +1
Economics, Econometrics and Finance · Mathematics · #62N01 #FOS: Mathematics #Financial Risk and Volatility Modeling #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistical Methods in Clinical Trials #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1401.7801
openalex publication_date 2014/01/30 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
Statistical inference in competing risks models is often based on the famous\nAalen-Johansen estimator. Since the corresponding limit process lacks\nindependent increments, it is typically applied together with Lin's (1997)\nresampling technique involving standard normal multipliers. Recently, it has\nbeen seen that this approach can be interpreted as a wild bootstrap technique\nand that other multipliers, as e.g. centered Poissons, may lead to better\nfinite sample performances, see Beyersmann et al. (2013). Since the latter is\nclosely related to Efron's classical bootstrap, the question arises whether\nthis or more general weighted bootstrap versions of Aalen-Johansen processes\nlead to valid results. Here we analyze their asymptotic behaviour and it turns\nout that such weighted bootstrap versions in general possess the wrong\ncovariance structure in the limit. However, we explain that the weighted\nbootstrap can nevertheless be applied for specific null hypotheses of interest\nand also discuss its limitations for statistical inference. To this end, we\nintroduce different consistent weighted bootstrap tests for the null hypothesis\nof stochastically ordered cumulative incidence functions and compare their\nfinite sample performance in a simulation study.\n