Abstract
A general asymptotic theory of estimates from estimating functions based on jack-knife pseudo-observations is established by requiring that the underlying estimator can be expressed as a smooth functional of the empirical distribution. Using results in p-variation norms, the theory is applied to important estimators from time-to-event analysis, namely the Kaplan–Meier estimator and the Aalen–Johansen estimator in a competing risks model, and the corresponding estimators of restricted mean survival and cause-specific lifetime lost. Under an assumption of completely independent censorings, this allows for estimating parameters in regression models of survival, cumulative incidences, restricted mean survival, and cause-specific lifetime lost. Considering estimators as functionals and applying results in p-variation norms is apparently an excellent way of studying the asymptotics of such estimators.
| Original language | English |
|---|---|
| Journal | Annals of Statistics |
| Volume | 45 |
| Issue | 5 |
| Pages (from-to) | 1988-2015 |
| Number of pages | 28 |
| ISSN | 0090-5364 |
| DOIs | |
| Publication status | Published - 31 Oct 2017 |
Keywords
- U-statistics
- functional differentiability
- p-variation
- pseudo-observation method
- pseudo-values
- von Mises expansion