Abstract

This paper provides an alternative imputation method to estimate the marginal mean and its variance for an outcome variable in the presence of missing values, when a set of fully observed covariates is available. For each unit with missing information, the imputed value is a weighted average of observed outcomes (the outcomes of the donors), where the weights are determined by solving a linear programming problem that minimizes the distance between a weighted average of the covariate values of the donors and the covariate value of the unit under analysis. Under the missing at random (MAR) assumption and suitable conditions, we show that the bias of the simple average of the completed outcome data, our estimator of the outcome mean, is $\sqrt{N}$-consistent with $N$ the sample size. Moreover, we also present an asymptotic normality result for this estimator and provide a consistent estimator for its variance. Finite sample properties of our proposal are investigated through Monte Carlos simulations. The STATA routine that implements our approach is also provided.