Semiparametric efficient empirical higher order influence function estimators

• DOI: 10.1920/wp.cem.2017.3017
• Publication Date: 2017-08-10T09:46:41Z
• Authors: James Robins; Rajarshi Mukherjee; Whitney K. Newey
• Keywords: Semiparametric model; Semiparametric regression

Robins et al. (2008Robins ( , 2016b) ) applied the theory of higher order influence functions (HOIFs) to derive an estimator mean outcome Y in a missing data model with at random conditional on vector X continuous covariates; their estimator, contrast previous estimators, is semiparametric efficient under minimal conditions.However (2008, depends non-parametric estimate density X.In this paper, we introduce new HOIF that has same asymptotic properties as but does not require nonparametric estimation multivariate density, which important because accurate high dimensional feasible moderate sample sizes often encountered applications.We also show our can be generalized entire class functionals considered by (2008) include average effect treatment response when suffices control confounding and expected variance given X.