Asymptotic theory of generalized estimating equations based on jack-knife pseudo-observations
Morten Overgaard, Erik Thorlund Parner, Jan Pedersen
The Annals of Statistics · 2017 · Volume 45 · Issue 5
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.
Keywords
62F12, 62J12, 62N02, functional differentiability, pseudo-observation method, Pseudo-values, p-variation, U-statistics, von Mises expansion
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