Asymptotic theory of generalized estimating equations based on jack-knife pseudo-observations

By Morten Storm Overgaard, E. Parner, Jan Pedersen. 2017

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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.

Subfields: Applied Mathematics, Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/58c115d8338a98e864ec05f3f8e64ca0bdae89e0