The Effect of Microaggregation by Individual Ranking on the Estimation of Moments

Microaggregation by individual ranking (IR) is an important technique for masking confidential data. While being a successful method for controlling the disclosure risk of observations, IR is also known for its favorable property of having a relatively small effect on the results of statistical analyses. In this paper we conduct a detailed theoretical analysis on the estimation of arbitrary moments from a data set that has been anonymized by means of the IR method. We show that classical moment estimators remain both consistent and asymptotically normal under relatively weak assumptions. This theory provides the justification for applying standard statistical estimation techniques to the anonymized data without having to correct for a possible bias caused by anonymization.