A Generally Efficient HAL-TMLE

Chapter
Part of the Springer Series in Statistics book series (SSS)

Abstract

We will present a TMLE of ψ0 that is asymptotically efficient at any \(P \in \mathcal{M}\). This is a remarkable statement since we only assume strong positivity, some global bounds, and a finite variation norm of \(\bar{Q}_{0},\bar{G}_{0}\). This estimation problem for the treatment specific mean will be our key example to demonstrate a general one-step TMLE that is guaranteed to be asymptotically efficient for any model and pathwise differentiable target parameter, essentially only assuming a positivity assumption, also guaranteeing strong identifiability of the target parameter.

References

  1. M.J. van der Laan, Targeted estimation of nuisance parameters to obtain valid statistical inference. Int. J. Biostat. 10(1), 29–57 (2014b)Google Scholar
  2. M.J. van der Laan, A generally efficient targeted minimum loss based estimator. Int. J. Biostat. 13(2), 1106–1118 (2017)Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Division of Biostatistics and Department of StatisticsUniversity of California, BerkeleyBerkeleyUSA

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