An equivalence result for moment equations when data are missing at random

Abstract

We consider general statistical models defined by moment equations when data are missing at random. Using the inverse probability weighting, such a model is shown to be equivalent with a model for the observed variables only, augmented by a moment condition defined by the missing mechanism. Our framework covers a large class of parametric and semiparametric models where we allow for missing responses, missing covariates and any combination of them. The equivalence result is stated under minimal technical conditions and sheds new light on various aspects of interest in the missing data literature, as for instance the efficiency bounds and the construction of the efficient estimators, the restricted estimators and the imputation.

Keywords

• efficiency bounds
• imputation
• inverse probability weighting
• semiparametric regression
• restricted estimators