Abstract
Using noise multiplied data to protect confidential data has recently drawn some attention. Understanding the probability property of the underlying confidential data based on their masked data is of interest in confidential data analysis. This paper proposes the approach of sample-moment-based density approximant based on noise multiplied data and provides a new manner for approximating the density function of the underlying confidential data without accessing the original data.
The approach of sample-moment-based density approximant is an extension of the approach of moment-based density approximant, which is mathematically equivalent to traditional orthogonal polynomials approaches to the probability density function (Provost, 2005). This paper shows that, regardless of a negligible probability, a moment-based density approximant can be well approximated by its sample-moment-based approximant if the size of the sample used in the evaluation is reasonable large. Consequently, a density function can be reasonably approximated by its sample-moment-based density approximant.
This paper focuses on the properties and the performance of the approach of the sample-moment-based density approximant based on noise multiplied data. Due to the restriction on the number of pages, some technical issues on implementing the approach proposed in practice will be discussed in another paper.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Duncan, G.T., Lambert, D.: Disclosure limited data dissemination (with comment). Journal of the American Statistical Association 81, 1–28 (1986)
Duncan, G.T., Lambert, D.: The risk of disclosure for microdata. Journal of Business and Economic Statistics 7, 207–217 (1989)
Evans, T.: Effects on Trend Statistics of the Use of Multiplicative Noise for Disclosure Limitation, US Bureau of the Census (1996), http://www.census.gov/srd/sdc/papers.html (accessed December 5, 2008)
Evans, T., Zayatz, L., Slanta, J.: Using Noise for Disclosure Limitation of Establishment Tabular Data. Journal of Official Statistics 14, 537–551 (1998)
Hwang, J.T.: Multiplicative errors-in-variables models with applications to recent data released by the U.S. Department of Energy. Journal of the American Statistical Association 81, 680–688 (1986)
Kim, J.J., Winkler, W.E.: Multiplicative Noise for Masking Continuous Data, Research Report Series (Statistics \(\sharp\)2003-01), Statistical Research Division, U.S. Bureau of the Census, Washington D.C. 20233 (2003)
Kim, J.J., Jeong, D.M.: Truncated triangular distribution for multiplicative noise and domain estimation, Section on Government Statistics - JSM 2008, pp. 1023–1030 (2008)
Klein, M., Sinha, B.: Statistical analysis of noise-multiplied data using multiple imputation. Journal of Official Statistics 29, 425–465 (2013)
Krisinich, F., Piesse, A.: Multiplicative Microdata Noise for Confidentialising Tables of Business Data: Application to AES99, Data with a Comparison to Cell Suppression, Research and Analytical Report 2002 #19, Statistics New Zealand (2002)
Lin, Y.-X., Wise, P.: Estimation of regression parameters from noise multiplied data. Journal of Privacy and Confidentiality 4, 55–88 (2012)
Mood, A.M., Graybill, F.A., Boes, D.C.: Introduction to the Theory of Statistics. McGraw-Hill, Singapore (1963)
Nayak, T.K., Sinha, B., Zayatz, L.: Statistical properties of multiplicative noise masking for confidentiality protection. Journal of Official Statistics 27, 527–544 (2011)
Oganian, A.: Multiplicative noise protocols. In: Domingo-Ferrer, J., Magkos, E. (eds.) PSD 2010. LNCS, vol. 6344, pp. 107–117. Springer, Heidelberg (2010)
Provost, S.B.: Moment-Based Density Approximants. The Mathematica Journal 9, 728–756 (2005)
Shlomo, N.: Releasing Microdata: Disclosure Risk Estimation, Data Masking and Assessing Utility. Journal of Privacy and Confidentiality 2, 73–91 (2010)
Sinha, B., Nayak, T.K., Zayatz, L.: Privacy protection and quantile estimation from noise multiplied data. Sankhya B 73, 297–315 (2011)
Willenborg, L., de Waal, T.: Elements of Statistical Disclosure Control. Lecture Notes in Statistics, vol. 155. Springer, New York (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Lin, YX. (2014). Density Approximant Based on Noise Multiplied Data. In: Domingo-Ferrer, J. (eds) Privacy in Statistical Databases. PSD 2014. Lecture Notes in Computer Science, vol 8744. Springer, Cham. https://doi.org/10.1007/978-3-319-11257-2_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-11257-2_8
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-11256-5
Online ISBN: 978-3-319-11257-2
eBook Packages: Computer ScienceComputer Science (R0)