Efficient estimation and stratified sampling

In this paper we investigate estimation of a class of semi-parametric models. The part of the model that is not specified is the marginal distribution of the explanatory variables. The sampling is stratified on the dependent variables, implying that the explanatory variables are no longer exogenous or ancillary. We develop a new estimator for this estimation problem and show that it achieves the semi-parametric efficiency bound for this case. In addition we show that the estimator applies to a number of sampling schemes that have previously been treated separately.