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Perturbation by multiplicative noise and the Simulation Extrapolation method

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Abstract

While most of the literature on measurement error focuses on additive measurement error, we consider in this paper the multiplicative case. We apply the Simulation Extrapolation method (SIMEX)—a procedure which was originally proposed by Cook and Stefanski (J. Am. Stat. Assoc. 89:1314–1328, 1994) in order to correct the bias due to additive measurement error—to the case where data are perturbed by multiplicative noise and present several approaches to account for multiplicative noise in the SIMEX procedure. Furthermore, we analyze how well these approaches reduce the bias caused by multiplicative perturbation. Using a binary probit model, we produce Monte Carlo evidence on how the reduction of data quality can be minimized.

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References

  • Carroll, R., Ruppert, D., Stefanski, L.: Measurement Error in Nonlinear Models. Chapman and Hall, London (1995)

    MATH  Google Scholar 

  • Carroll, R., Kuechenhoff, H., Lombard, F., Stefanski, L.: Asymptotics for the simex estimator in structural measurement error models. J. Am. Stat. Assoc. 91, 242–250 (1996)

    Article  MATH  Google Scholar 

  • Cook, J., Stefanski, L.: A simulation extrapolation method for parametric measurement error models. J. Am. Stat. Assoc. 89, 1314–1328 (1994)

    Article  MATH  Google Scholar 

  • Fuller, W.: Measurement Error Models. Wiley, New York (1987)

    MATH  Google Scholar 

  • Hwang, J.T.: Multiplicative errors-in-variables models with applications to recent data released by the US Department of Energy. J. Am. Stat. Assoc. 81, 680–688 (1986)

    Article  MATH  Google Scholar 

  • Iturria, S., Carroll, R., Firth, D.: Polynomial regression and estimating functions in the presence of multiplicative measurement error. J. R. Stat. Soc. Ser. B Stat. Methodol. 61, 547–561 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  • Lin, A.: Estimation of multiplicative measurement-error models and some simulation results. Econ. Lett. 317, 13–20 (1989)

    Article  Google Scholar 

  • Lyles, R., Kupper, L.: A detailed evaluation of adjustment methods for multiplicative measurement error in linear regression with applications in occupational epidemiology. Biometrics 53, 1008–1025 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  • Nolte, S.: The multiplicative simulation extrapolation approach. Working Paper, University of Konstanz (2007). http://papers.ssrn.com/sol3/papers.cfm?abstract_id=969599

  • Ronning, G., et al.: Handbuch zur Anonymisierung wirtschaftsstatistischer Mikrodaten. Statistisches Bundesamt, Wiesbaden, Reihe “Statistik und Wissenschaft”, Band 4 (2005), (with R. Sturm, J. Höhne, R. Lenz, M. Rosemann, M. Scheffler, D. Vorgrimler)

  • Rosemann, M.: Auswirkungen datenverändernder Anonymisierungsverfahren auf die Analyse von Mikrodaten. IAW-Report, Nr. 66. Institut für Angewandte Wirtschaftsforschung (2006)

  • Stefanski, L., Cook, J.: Simulation-extrapolation: the measurement error jackknife. J. Am. Stat. Assoc. 90(432), 1247–1256 (1995)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Institute for Applied Economic Research (IAW), Ob dem Himmelreich 1, 72074, Tuebingen, Germany

    Elena Biewen & Martin Rosemann

  2. Department of Economics, University of Konstanz, Box D124, 78457, Konstanz, Germany

    Sandra Nolte

Authors
  1. Elena Biewen
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  2. Sandra Nolte
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  3. Martin Rosemann
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Corresponding author

Correspondence to Elena Biewen.

Additional information

For helpful comments, we would like to thank Helmut Küchenhoff, Winfried Pohlmeier, and Gerd Ronning. Sandra Nolte gratefully acknowledges financial support by the DFG. Elena Biewen and Martin Rosemann gratefully acknowledge the financial support by the Federal Ministry of Education and Research (BMBF). The usual disclaimer applies.

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Biewen, E., Nolte, S. & Rosemann, M. Perturbation by multiplicative noise and the Simulation Extrapolation method. AStA Adv Stat Anal 92, 375–389 (2008). https://doi.org/10.1007/s10182-008-0089-7

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  • DOI: https://doi.org/10.1007/s10182-008-0089-7

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