Efficiency for heteroscedastic regression with responses missing at random

Heteroscedastic regression models are commonly used when the error variance differs across observations, i.e. when the error distribution depends on covariate values. We consider such models with responses possibly missing at random and show that functionals of the conditional distribution of the response given the covariates can be estimated efficiently using complete case analysis. We provide a formula for the efficient influence function in the general semiparametric heteroscedastic regression model and discuss special cases and examples.