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From Marginals to Array Structure with the Shuttle Algorithm

Author

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  • Buzzigoli, Lucia
  • Giusti, Antonio

Abstract

In many statistical problems there is the need to analyze the structure of an unknown n-dimensional array given its marginal distributions. The usual method utilized to solve the problem is linear programming, which involves a large amount of computational time when the original array is large. Alternative solutions have been proposed in the literature, especially to find less time consuming algorithms. One of these is the shuttle algorithm introduced by Buzzigoli and Giusti [1] to calculate lower and upper bounds of the elements of an n-way array, starting from the complete set of its (n-1)-way marginals. The proposed algorithm, very easy to implement with a matrix language, shows interesting properties and possibilities of application. The paper presents the algorithm, analyses its properties and describes its disadvantages. It also suggests possible applications in some statistical fields and, in particular, in Symbolic Data Analysis and, finally, shows the results of some simulations on randomly generated arrays.

Suggested Citation

  • Buzzigoli, Lucia & Giusti, Antonio, 2006. "From Marginals to Array Structure with the Shuttle Algorithm," MPRA Paper 49245, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:49245
    as

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    References listed on IDEAS

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    1. Sumit Dutta Chowdhury & George T. Duncan & Ramayya Krishnan & Stephen F. Roehrig & Sumitra Mukherjee, 1999. "Disclosure Detection in Multivariate Categorical Databases: Auditing Confidentiality Protection Through Two New Matrix Operators," Management Science, INFORMS, vol. 45(12), pages 1710-1723, December.
    2. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(2), pages 427-429, April.
    3. Billard L. & Diday E., 2003. "From the Statistics of Data to the Statistics of Knowledge: Symbolic Data Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 470-487, January.
    4. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(1), pages 223-229, February.
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    More about this item

    Keywords

    Shuttle algorithm; Linear programming; Statistical disclosure control; Linked tables; Zero restrictions;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C88 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Other Computer Software

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