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Estimation of a linear model in transformed variables under microaggregation by individual ranking

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Abstract

We consider the least squares estimation of a linear regression model in transformed variables from a data set that has been microaggregated by means of the individual ranking method. It is shown that the least squares estimators are consistent even in the case where variable transformations are carried out after microaggregation. Applying individual ranking techniques to a data set thus guarantees the analytical validity of the microaggregated data for a wide class of statistical models.

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References

  • Biewen, E.: Individual Ranking und multiplikative Überlagerung im Modell mit fixen Effekten. Unpublished manuscript, Institut für Angewandte Wirtschaftsforschung, Tübingen (2007)

  • de Boor, C.: A Practical Guide to Splines. Springer, New York (1978)

    MATH  Google Scholar 

  • Defays, D., Anwar, M.N.: Masking microdata using microaggregation. J. Off. Stat. 14(4), 449–461 (1998)

    Google Scholar 

  • Domingo-Ferrer, J., Oganian, A., Torres, A., Mateo-Sanz, J.M.: On the security of microaggregation with individual ranking: Analytical attacks. Int. J. Uncertainty Fuzziness Knowledge-Based Syst. 10(5), 477–491 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  • Domingo-Ferrer, J., Torra, V.: A quantitative comparison of disclosure control methods for microdata. In: Doyle, P., Lane, J., Theeuwes, J., Zayatz, L. (eds.) Confidentiality, Disclosure, and Data Access, pp. 111–133. North-Holland, Amsterdam (2001)

    Google Scholar 

  • Fritsch, M., Stephan, A.: Die Heterogenität der technischen Effizienz innerhalb von Wirtschaftszweigen—Auswertungen auf Grundlage der Kostenstrukturstatistik des Statistischen Bundesamtes. In: Pohl, R., Fischer, J., Rockmann, U., Semlinger, K. (eds.) Analysen zur regionalen Industrieentwicklung—Sonderauswertungen einzelbetrieblicher Daten der amtlichen Statistik, pp. 143–156. Statistisches Landesamt, Berlin (2003)

    Google Scholar 

  • Hastie, T., Tibshirani, R.: Generalized Additive Models. Chapman & Hall, London (1990)

    MATH  Google Scholar 

  • Ronning, G., Sturm, R., Höhne, J., Lenz, R., Rosemann, M., Scheffler, M., Vorgrimler, D.: Handbuch zur Anonymisierung wirtschaftsstatistischer Mikrodaten. Statistik und Wissenschaft, vol. 4. Statistisches Bundesamt, Wiesbaden (2005)

    Google Scholar 

  • Rosemann, M.: Erste Ergebnisse von vergleichenden Untersuchungen mit anonymisierten und nicht anonymisierten Einzeldaten am Beispiel der Kostenstrukturerhebung und der Umsatzsteuerstatistik. In: Ronning, G., Gnoss, R. (eds.) Anonymisierung wirtschaftsstatistischer Einzeldaten. Forum der Bundesstatistik, vol. 42, pp. 154–183. Statistisches Bundesamt, Wiesbaden (2003)

    Google Scholar 

  • Schmid, M.: Estimation of a linear model under microaggregation by individual ranking. Allgemeines Stat. Arch. 90(3), 419–438 (2006)

    Article  MATH  Google Scholar 

  • Schmid, M., Schneeweiss, H.: The effect of microaggregation procedures on the estimation of linear models: A simulation study. In: Pohlmeier, W., Ronning, G., Wagner, J. (eds.) Econometrics of Anonymized Micro Data. Jahrbücher für Nationalökonomie und Statistik, vol. 225(5), pp. 529–543. Lucius & Lucius, Stuttgart (2005)

    Google Scholar 

  • Schmid, M., Schneeweiss, H., Küchenhoff, H.: Estimation of a linear regression under microaggregation with the response variable as a sorting variable. Stat. Neerlandica 61(4), 407–431 (2007)

    Article  Google Scholar 

  • Willenborg, L., de Waal, T.: Elements of Statistical Disclosure Control. Springer, New York (2001)

    MATH  Google Scholar 

  • Winkler, W.E.: Single-ranking micro-aggregation and reidentification. Statistical Research Division Report RR 2002/08, US Bureau of the Census, Washington (2002)

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Authors and Affiliations

  1. Institut für Medizininformatik, Biometrie und Epidemiologie, Friedrich-Alexander-Universität Erlangen-Nürnberg, Waldstraße 6, 91054, Erlangen, Germany

    Matthias Schmid

  2. Institut für Statistik, Ludwig-Maximilians-Universität München, Ludwigstraße 33, 80539, München, Germany

    Hans Schneeweiss

Authors
  1. Matthias Schmid
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  2. Hans Schneeweiss
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Correspondence to Matthias Schmid.

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Schmid, M., Schneeweiss, H. Estimation of a linear model in transformed variables under microaggregation by individual ranking. AStA Adv Stat Anal 92, 359–374 (2008). https://doi.org/10.1007/s10182-008-0087-9

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  • DOI: https://doi.org/10.1007/s10182-008-0087-9

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