Efficient estimators for expectations in nonlinear parametric regression models with responses missing at random

Abstract

We consider nonlinear regression models that are solely defined by a parametric model for the regression function. The responses are assumed to be missing at random, with the missingness depending on multiple covariates. We propose estimators for expectations of a known function of response and covariates. Our estimator is a nonparametric estimator corrected for the regression function. We show that it is asymptotically efficient in the Hájek and Le Cam sense. Simulations and an example using real data confirm the optimality of our approach.