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Perturbation of Numerical Confidential Data via Skew-t Distributions

Author

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  • Seokho Lee

    (Department of Biostatistics, Harvard School of Public Health, Boston, Massachusetts 02115)

  • Marc G. Genton

    (Department of Statistics, Texas A& M University, College Station, Texas 77843)

  • Reinaldo B. Arellano-Valle

    (Departamento de Estadística, Facultad de Matemática, Pontificia Universidad Católica de Chile, Santiago 22, Chile)

Abstract

We propose a new data perturbation method for numerical database security problems based on skew-t distributions. Unlike the normal distribution, the more general class of skew-t distributions is a flexible parametric multivariate family that can model skewness and heavy tails in the data. Because databases having a normal distribution are seldom encountered in practice, the newly proposed approach, coined the skew-t data perturbation (STDP) method, is of great interest for database managers. We also discuss how to preserve the sample mean vector and sample covariance matrix exactly for any data perturbation method. We investigate the performance of the STDP method by means of a Monte Carlo simulation study and compare it with other existing perturbation methods. Of particular importance is the ability of STDP to reproduce characteristics of the joint tails of the distribution in order for database users to answer higher-level questions. We apply the STDP method to a medical database related to breast cancer.

Suggested Citation

  • Seokho Lee & Marc G. Genton & Reinaldo B. Arellano-Valle, 2010. "Perturbation of Numerical Confidential Data via Skew-t Distributions," Management Science, INFORMS, vol. 56(2), pages 318-333, February.
    • Handle: RePEc:inm:ormnsc:v:56:y:2010:i:2:p:318-333
    DOI: 10.1287/mnsc.1090.1104
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    References listed on IDEAS

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    6. Chu, Amanda M.Y. & Ip, Chun Yin & Lam, Benson S.Y. & So, Mike K.P., 2022. "Vine copula statistical disclosure control for mixed-type data," Computational Statistics & Data Analysis, Elsevier, vol. 176(C).
    7. Trottini, Mario & Muralidhar, Krish & Sarathy, Rathindra, 2011. "Maintaining tail dependence in data shuffling using t copula," Statistics & Probability Letters, Elsevier, vol. 81(3), pages 420-428, March.
    8. Contreras-Reyes, Javier E., 2014. "Asymptotic form of the Kullback–Leibler divergence for multivariate asymmetric heavy-tailed distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 200-208.
    9. Yi Qian & Hui Xie, 2015. "Drive More Effective Data-Based Innovations: Enhancing the Utility of Secure Databases," Management Science, INFORMS, vol. 61(3), pages 520-541, March.
    10. Haibing Lu & Jaideep Vaidya & Vijayalakshmi Atluri & Yingjiu Li, 2015. "Statistical Database Auditing Without Query Denial Threat," INFORMS Journal on Computing, INFORMS, vol. 27(1), pages 20-34, February.

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