A Falsifiability Characterization of Double Robustness Through Logical Operators

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Abstract

We address the characterization of problems in which a consistent estimator exists in a union of two models, also termed as a doubly robust estimator. Such estimators are important in missing information, including causal inference problems. Existing characterizations, based on the semiparametric theory of projections, have seen sufficient progress, but can still leave one's understanding less than satisfied as to when and especially why such estimation works. We explore here a different, explanatory characterization - an exegesis based on logical operators. We show that double robustness exists if and only if we can produce consistent estimators for each contributing model based on an "AND" estimator, i. e., an estimator whose consistency generally needs both models to be correct. We show how this characterization explains double robustness through falsifiability.

Original languageEnglish (US)
Article number20180016
JournalJournal of Causal Inference
Volume7
Issue number1
DOIs
StatePublished - Mar 1 2019

Keywords

  • double robustness
  • logical operators

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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