Discrete models for data imputation

The paper is concerned with the problem of automatic detection and correction of inconsistent or out of range data in a general process of statistical data collection. The proposed approach is able to deal with hierarchical data containing both qualitative and quantitative values. As customary, erroneous data records are detected by formulating a set of rules. Erroneous records should then be corrected, by modifying as less as possible the erroneous data, while causing minimum perturbation to the original frequency distributions of the data. Such process is called imputation. By encoding the rules with linear inequalities, we convert imputation problems into integer linear programming problems. The proposed procedure is tested on a real-world case of census. Results are extremely encouraging both from the computational and from the data quality point of view