Journal of Official Statistics, Vol.25, No.4, 2009. pp. 529548

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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 microdata. Observations in a data set are grouped and replaced by their corresponding group means, so that identification of sensitive observations is unlikely. However, microaggregation is also known to affect the results of statistical analyses. In this article we investigate the impact of microaggregation on the least squares estimation of a linear model in continuous variables. It is shown that least squares estimators are not necessarily consistent if the groups of observations are formed by means of a sorting variable. 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.

Asymptotic variance, consistent estimation, disclosure control, linear model, microaggregation, sorting variable

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