We consider general statistical models defined by moment equations when data are missing atrandom. Using the inverse probability weighting, such a model is shown to be equivalent with amodel for the observed variables...We consider general statistical models defined by moment equations when data are missing atrandom. Using the inverse probability weighting, such a model is shown to be equivalent with amodel 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 modelswhere we allow for missing responses, missing covariates and any combination of them. Theequivalence result is stated under minimal technical conditions and sheds new light on variousaspects of interest in the missing data literature, as for instance the efficiency bounds and theconstruction of the efficient estimators, the restricted estimators and the imputation.展开更多
文摘We consider general statistical models defined by moment equations when data are missing atrandom. Using the inverse probability weighting, such a model is shown to be equivalent with amodel 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 modelswhere we allow for missing responses, missing covariates and any combination of them. Theequivalence result is stated under minimal technical conditions and sheds new light on variousaspects of interest in the missing data literature, as for instance the efficiency bounds and theconstruction of the efficient estimators, the restricted estimators and the imputation.
