Abstract
We will present a TMLE of ψ 0 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.
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References
M.J. van der Laan, Targeted estimation of nuisance parameters to obtain valid statistical inference. Int. J. Biostat. 10(1), 29–57 (2014b)
M.J. van der Laan, A generally efficient targeted minimum loss based estimator. Int. J. Biostat. 13(2), 1106–1118 (2017)
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van der Laan, M.J. (2018). A Generally Efficient HAL-TMLE. In: Targeted Learning in Data Science. Springer Series in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-65304-4_7
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DOI: https://doi.org/10.1007/978-3-319-65304-4_7
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