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Probability and quantile estimation from individually micro-aggregated data


  • Hans Schneeweiss


  • Daniel Rost


  • Matthias Schmid



Micro-aggregation is a frequently used strategy to anonymize data before they are released to the scientific public. A sample of a continuous random variable is individually micro-aggregated by first sorting and grouping the data into groups of equal size and then replacing the values of the variable in each group by their group mean. In a similar way, data with more than one variable can be anonymized by individual micro-aggregation. Data thus distorted may still be used for statistical analysis. We show that if probabilities and quantiles are estimated in the usual way by computing relative frequencies and sample quantiles, respectively, these estimates are consistent and asymptotically normal under mild conditions. Copyright Springer-Verlag 2012

Suggested Citation

  • 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.
  • Handle: RePEc:spr:metrik:v:75:y:2012:i:6:p:721-742
    DOI: 10.1007/s00184-011-0349-5

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    References listed on IDEAS

    1. Matthias Schmid, 2006. "Estimation of a linear model under microaggregation by individual ranking," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 90(3), pages 419-438, September.
    2. 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.
    3. Matthias Schmid & Hans Schneeweiss & Helmut K├╝chenhoff, 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.
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