Estimation of a Linear Regression under Microaggregation with the Response Variable as a Sorting Variable

Microaggregation is one of the most frequently applied statistical
disclosure control techniques for continuous data. The basic
principle of microaggregation is to group the observations in a
data set and to replace them by their corresponding group means.
However, while reducing the disclosure risk of data files, the
technique also affects the results of statistical analyses. The
paper deals with the impact of microaggregation on a linear model
in continuous variables. We show that parameter estimates are
biased if the dependent variable is used to form the groups. Using
this result, we develop a consistent estimator that removes the
aggregation bias. Moreover, we derive the asymptotic covariance
matrix of the corrected least squares estimator.