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Estimation of a linear regression under microaggregation with the response variable as a sorting variable

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  • Matthias Schmid
  • Hans Schneeweiss
  • Helmut Küchenhoff

Abstract

Microaggregation is a popular statistical disclosure control technique 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 multiple linear regression 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, and derive its asymptotic covariance matrix.

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  • Matthias Schmid & Hans Schneeweiss & Helmut Küchenhoff, 2007. "Estimation of a linear regression under microaggregation with the response variable as a sorting variable," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 61(4), pages 407-431, November.
    • Handle: RePEc:bla:stanee:v:61:y:2007:i:4:p:407-431
    DOI: 10.1111/j.1467-9574.2007.00366.x
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    References listed on IDEAS

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    1. Schmid Matthias & Schneeweiss Hans, 2005. "The Effect of Microaggregation Procedures on the Estimation of Linear Models: A Simulation Study," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 225(5), pages 529-543, October.
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    Cited by:

    1. Hans Schneeweiss & Daniel Rost & Matthias Schmid, 2012. "Probability and quantile estimation from individually micro-aggregated data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(6), pages 721-742, August.
    2. Thomas Augustin & Helmut Küchenhoff & Matthias Schmid, 2022. "Nachruf Hans Schneeweiß," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 16(2), pages 149-154, June.
    3. Schmid, Matthias & Schneeweiss, Hans, 2009. "The effect of microaggregation by individual ranking on the estimation of moments," Journal of Econometrics, Elsevier, vol. 153(2), pages 174-182, December.

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