期刊
ANNALS OF STATISTICS
卷 45, 期 5, 页码 1988-2015出版社
INST MATHEMATICAL STATISTICS
DOI: 10.1214/16-AOS1516
关键词
Pseudo-values; functional differentiability; von Mises expansion; pseudo-observation method; p-variation; U-statistics
资金
- Danish Council for Independent Research [DFF-4002-00003]
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.
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