Sequentially Debiased Estimation of Identified Total Effects in Causal Graphical Models with Hidden Variables

• Activity Number: 47 - Causal Inference in the Presence of Nuisance Parameters: Latest Developments
• Type: Invited
• Date/Time: Sunday, August 7, 2022 : 4:00 PM to 5:50 PM
• Sponsor: IMS
• Author(s): Andrea ROTNITZKY* and Ezequiel Smucler and James M Robins
• Companies: Universidad Torcuato Di Tella and Glovo and Harvard University
• Keywords: one-step estimation; influence functions; ID algorithm; causal graphical models; debiased estimation; root-n consistency

Abstract

We consider estimation of the total effect of time dependent treatments on an outcome assuming a causal graphical model with hidden variables. The ID algorithm (Tian and Pearl, 2002) determines if the effect is identified and when it is, it returns a functional ?(P) of the observed data law P that identifies it. Because ?(P) typically depends on infinite dimensional parameters, such as conditional means or densities, plug-in estimators ?(P_{n}) do not converge at rate root-n for most non-parametric estimators P_{n} of P. One-step cross-fitted estimation is a well known strategy for correcting the bias of ?(P_{n}) and hopefully yielding root-n consistent estimation. It is based on adding to ?(P_{n}) the empirical mean of an estimator of the influence function of ?(P) with unknown nuisance functionals ?(P) estimated by plug-in from an independent sample. In this talk we argue that we can significantly improve upon one-step cross-fitted estimators that depend on plug-in estimators of ?(P) by considering estimators of ?(P) that minimize an objective function which is itself a debiased estimator of a population objective function that is minimized at ?(P)