Abstract
In this paper we address two inferential aspects of noise multiplied magnitude microdata. First, in the context of disclosure risk assessment of tabular magnitude data, we study the consequences of noise multiplication when an intruder tries to speculate a target unit’s value in a cell based on knowledge of the perturbed cell total and values of some units within the cell. This is related to some results in Nayak et al. (J Off Stat, 2011). Second, we develop Bayesian methods to infer about a quantile of a microdata set based on their noise perturbed values. Natural applications include estimation of quartiles and median of an original microdata set when only their noise perturbed versions are available.
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References
Blumenthal, S., and A. Cohen. 1968a. Estimation of the larger translation parameter. Annals of mathematical statistics 39:502–516.
Blumenthal, S., and A. Cohen. 1968b. Estimation of the larger of two normal means. Annals of mathematical statistics 39:861–876.
Brand, R. 2002. Microdata protection through noise addition. In Inference control in statistical databases, ed. J. Domingo-Ferrer, pp. 97–116. Berlin: Springer.
Doyle, P., J. Lane, J. Theeuwes, and L. Zayatz. eds. 2001. Confidentiality, disclosure and data access: Theory and practical applications for statistical agencies. Amsterdam: Elsevier.
Dudewicz, E.J. 1971a. Maximum likelihood estimators for non-1-1 functions. Trabojos de Estadistica y de Investigacion Operativa 22:65–70.
Dudewicz, E.J. 1971b. Maximum likelihood estimators for ranked means. Zeitschrift fūr Wahrscheinlichkeitstheorie und Verwandte Gebiete, 19, 29–42.
Duncan, G.T., and S.E. Fienberg. 1999. Obtaining information while preserving privacy: A Markov perturbation method for tabular data. In Eurostat statistical data protection ’98 Lisbon, pp. 351–362. Luxembourg: Eurostat.
Duncan, G.T., and S. Mukherjee. 2000. Optimal disclosure limitation strategy in statistical databases: Deterring tracker attacks through additive noise. Journal of the American Statistical Association 95:720–729.
Duncan, G.T., and S.L. Stokes. 2004. Disclosure risk vs. data utility: The R-U confidentiality map as applied to topcoding. Chance, 17:16–20.
Elfessi, A., and N. Pal. 1992. Estimation of the smaller and larger of two uniform scale parameters. Communications in Statistics. Theory and Methods 21:2997–3015.
Evans, T., L. Zayatz, and J. Slanta. 1998. Using noise for disclosure limitation of establishment tabular data. Journal of Official Statistics 4:537–551.
Fong, D.K.H. 1987. Ranking and estimation of exchangeable means in balanced and unbalanced models: A Bayesian aproach. Ph.D. thesis, Purdue University.
Fong, D.K.H. 1992. A Bayesian approach to the estimation of the largest normal mean. Journal of Statistical Computation and Simulation 40:119–133.
Fuller, W.A. 1993. Masking procedures for microdata disclosure limitation. Journal of Official Statistics 9:383–406.
Givens, G.H., and J.A. Hoeting 2005. Computational statistics. New York: John Wiley.
Karr, A.F., C.N. Kohnen, A. Oganian, J.P. Reiter, and A.P. Sanil. 2006. A framework for evaluating the utility of data altered to protect confidentiality. American Statistician 60:224–232.
Kim, J. 1986. A method for limiting disclosure in microdata based on random noise and transformation. In Proceedings of the American Statistical Association, Section on Survey Research Methods, pp. 303–308.
Kim, J.J., and W.E. Winkler. 2003. Multiplicative noise for masking continuous data. Technical Report Statistics #2003-01, Statistical Research Division, U.S. Bureau of the Census, Washington D.C.
Kumar, S., and D. Sharma. 1993. Unbiased inestimability of ordered parameters. Statistics 24:137–142.
Little, R.J.A. 1993. Statistical analysis of masked data. Journal of Official Statistics 9:407–426.
Misra, N., R. Anand, and H. Singh. 1997. Estimation of the smaller and larger scale parameters of two exponential distributions. Statistics and Decisions 15:75–98.
Nayak, T., B. Sinha, and L. Zayatz. 2011. Statistical properties of multiplicative noise masking for confidentiality protection. Journal of Official Statistics 27:527–544..
Shao, J. 1999. Mathematical statistics. New York: Springer.
Tendick, P. 1991. Optimal noise addition for preserving confidentiality in multivariate data. Journal of Statistical Planning and Inference 27:341–353.
van Eeden, C. 2006. Restricted parameter space estimation problems. New York: Springer.
Willenborg, L.C.R.J., and T. De Waal. 2001. Elements of statistical disclosure control. New York: Springer.
Yancey, W.E., W.E. Winkler, and R.H. Creecy. 2002. Disclosure risk assessment in perturbative microdata protection. In Inference control in statistical databases, ed. J. Domingo-Ferrer, pp. 135–152. Springer.
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This report is released to inform interested parties of ongoing research and to encourage discussion of work in progress. The views expressed in the paper are those of the authors and not necessarily those of the U.S. Census Bureau.
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Sinha, B., Nayak, T.K. & Zayatz, L. Privacy protection and quantile estimation from noise multiplied data. Sankhya B 73, 297–315 (2011). https://doi.org/10.1007/s13571-011-0030-z
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DOI: https://doi.org/10.1007/s13571-011-0030-z