One-Step TMLE

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

Abstract

In this chapter, we will present one-dimensional universal least favorable parametric submodels for the TMLE of univariate and multivariate target parameters. They guarantee that a single TMLE-update of the initial estimator already solves the efficient influence curve equation. We explain why this type of one-step TMLE is more stable than an iterative TMLE. By the fact that the one-step TMLE for high-dimensional or even infinite-dimensional target parameters is a substitution estimator, it follows that it completely respects the structure of the infinite dimensional parameter. The content of this chapter partly relies on van der Laan and Gruber (2016). As an example, we present a one-step TMLE of a complete treatment-specific survival function.

References

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Mark J. van der Laan
    • 1
  • Wilson Cai
    • 2
  • Susan Gruber
    • 3
  1. 1.Division of Biostatistics and Department of StatisticsUniversity of California, BerkeleyBerkeleyUSA
  2. 2.Division of BiostatisticsUniversity of California, BerkeleyBerkeleyUSA
  3. 3.Department of Population MedicineHarvard Medical School, Harvard Pilgrim Health Care InstituteBostonUSA

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