In a paper published in the Journal of the American Statistical Association, we developed an approach that fully integrates editing and imputation for continuous microdata under linear constraints. The approach relies on a Bayesian hierarchical model that includes (i) a flexible joint probability model for the underlying true values of the data with support only on the set of values that satisfy all editing constraints, (ii) a model for latent indicators of the variables that are in error, and (iii) a model for the reported responses for variables in error.  An R package implementing the model is available on CRAN and linked on the Downloadable Software page on this site.

in the Journal of the American Statistical Association