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A column-oriented optimization approach for the generation of correlated random vectors

Author

Listed:
  • Jorge A. Sefair

    (Arizona State University)

  • Oscar Guaje

    (Universidad de los Andes)

  • Andrés L. Medaglia

    (Universidad de los Andes)

Abstract

To induce a desired correlation structure among random variables, widely popular simulation software relies upon the method of Iman and Conover (IC). The underlying premise is that the induced Spearman rank correlation is a meaningful way to approximate other correlation measures among the random variables (e.g., Pearson’s correlation). However, as expected, the desired a posteriori correlation structure often deviates from the Spearman correlation structure. Rooted in the same principle of IC, we propose an alternative distribution-free method based on mixed-integer programming to induce a Pearson correlation structure to bivariate or multivariate random vectors. We also extend our distribution-free method to other correlation measures such as Kendall’s coefficient of concordance, Phi correlation coefficient, and relative risk. We illustrate our method in four different contexts: (1) the simulation of a healthcare facility, (2) the analysis of a manufacturing tandem queue, (3) the imputation of correlated missing data in statistical analysis, and (4) the estimation of the budget overrun risk in a construction project. We also explore the limits of our algorithms by conducting extensive experiments using randomly generated data from multiple distributions.

Suggested Citation

  • Jorge A. Sefair & Oscar Guaje & Andrés L. Medaglia, 2021. "A column-oriented optimization approach for the generation of correlated random vectors," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(3), pages 777-808, September.
    • Handle: RePEc:spr:orspec:v:43:y:2021:i:3:d:10.1007_s00291-021-00620-5
    DOI: 10.1007/s00291-021-00620-5
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    References listed on IDEAS

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    1. Nasr, Walid W. & Maddah, Bacel, 2015. "Continuous (s, S) policy with MMPP correlated demand," European Journal of Operational Research, Elsevier, vol. 246(3), pages 874-885.
    2. Biswas, Atanu, 2004. "Generating correlated ordinal categorical random samples," Statistics & Probability Letters, Elsevier, vol. 70(1), pages 25-35, October.
    3. Kaeyoung Shin & Raghu Pasupathy, 2010. "An Algorithm for Fast Generation of Bivariate Poisson Random Vectors," INFORMS Journal on Computing, INFORMS, vol. 22(1), pages 81-92, February.
    4. Bahjat F. Qaqish, 2003. "A family of multivariate binary distributions for simulating correlated binary variables with specified marginal means and correlations," Biometrika, Biometrika Trust, vol. 90(2), pages 455-463, June.
    5. Raymond R. Hill & Charles H. Reilly, 2000. "The Effects of Coefficient Correlation Structure in Two-Dimensional Knapsack Problems on Solution Procedure Performance," Management Science, INFORMS, vol. 46(2), pages 302-317, February.
    6. Charles H. Reilly, 2009. "Synthetic Optimization Problem Generation: Show Us the Correlations!," INFORMS Journal on Computing, INFORMS, vol. 21(3), pages 458-467, August.
    7. Kolev, Nikolai & Paiva, Delhi, 2008. "Random sums of exchangeable variables and actuarial applications," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 147-153, February.
    8. Bruce W. Schmeiser & Ram Lal, 1982. "Bivariate Gamma Random Vectors," Operations Research, INFORMS, vol. 30(2), pages 355-374, April.
    9. Qing Xiao, 2017. "Generating correlated random vector involving discrete variables," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(4), pages 1594-1605, February.
    10. Philip M. Lurie & Matthew S. Goldberg, 1998. "An Approximate Method for Sampling Correlated Random Variables from Partially-Specified Distributions," Management Science, INFORMS, vol. 44(2), pages 203-218, February.
    11. Dias, Carlos Tadeu dos Santos & Samaranayaka, Ari & Manly, Bryan, 2008. "On the use of correlated beta random variables with animal population modelling," Ecological Modelling, Elsevier, vol. 215(4), pages 293-300.
    12. Arnab Chakraborty, 2006. "Generating multivariate correlated samples," Computational Statistics, Springer, vol. 21(1), pages 103-119, March.
    13. Yoshiaki Toyoda, 1975. "A Simplified Algorithm for Obtaining Approximate Solutions to Zero-One Programming Problems," Management Science, INFORMS, vol. 21(12), pages 1417-1427, August.
    14. Marco E. Lübbecke & Jacques Desrosiers, 2005. "Selected Topics in Column Generation," Operations Research, INFORMS, vol. 53(6), pages 1007-1023, December.
    15. Shults, Justine, 2017. "Simulating longer vectors of correlated binary random variables via multinomial sampling," Computational Statistics & Data Analysis, Elsevier, vol. 114(C), pages 1-11.
    16. Sefair, Jorge A. & Méndez, Carlos Y. & Babat, Onur & Medaglia, Andrés L. & Zuluaga, Luis F., 2017. "Linear solution schemes for Mean-SemiVariance Project portfolio selection problems: An application in the oil and gas industry," Omega, Elsevier, vol. 68(C), pages 39-48.
    17. C. R. Mitchell & A. S. Paulson & C. A. Beswick, 1977. "The effect of correlated exponential service times on single server tandem queues," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 24(1), pages 95-112, March.
    18. van der Geest, P. A. G., 1998. "An algorithm to generate samples of multi-variate distributions with correlated marginals," Computational Statistics & Data Analysis, Elsevier, vol. 27(3), pages 271-289, May.
    19. Zhang, Yufeng & Khani, Alireza, 2019. "An algorithm for reliable shortest path problem with travel time correlations," Transportation Research Part B: Methodological, Elsevier, vol. 121(C), pages 92-113.
    20. Charles N. Haas, 1999. "On Modeling Correlated Random Variables in Risk Assessment," Risk Analysis, John Wiley & Sons, vol. 19(6), pages 1205-1214, December.
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