Imputation of continuous variables missing at random using the method of simulated scores

For multivariate datasets with missing values, we present a procedure of statistical inference and state its "optimal" properties. Two main assumptions are needed: (1) data are missing at random (MAR); (2) the data generating process is a multivariate normal linear regression. Disentangling the problem of convergence of the iterative estimation/imputation procedure, we show that the estimator is a "method of simulated scores" (a particular case of McFadden's "method of simulated moments"); thus the estimator is equivalent to maximum likelihood if the number of replications is conveniently large, and the whole procedure can be considered an optimal parametric technique for imputation of missing data.