The Effect of Single-Axis Sorting on the Estimation of a Linear Regression

Microaggregation is one of the most important 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. In
this paper, we consider single-axis sorting, a frequently applied
microaggregation technique where the formation of groups depends on
the magnitude of a sorting variable related to the variables in the
data set. The paper deals with the impact of this technique on a
linear model in continuous variables. We show that parameter
estimates are asymptotically biased if the sorting variable depends
on the response variable of the linear model. 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.