Efficient Estimators for Expectations in Conditional Mean Models with Responses Missing at Random
Guorong Dai, Texas A&M University, USA
We consider regression models in which only the mean response given the covariates and the regression function is modeled parametrically. This model is useful when restrictive assumptions on the structure of the random errors cannot be justified. We propose estimators for expectations of the joint distribution of response and covariates when responses are possibly missing, with the missingness explained by the covariates. Our estimator is a non-parametric estimator involving a Nadaraya-Watson type estimator for conditional expectations, improved by an additive correction term that takes into account the non-linear regression structure. We prove that the estimator is asymptotically efficient in the Hajek and Le Cam sense. Simulations and an example using real data confirm the optimality of our approach.