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Application of threshold accepting to the evaluation of the discrepancy of a set of points

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  • Winker, Peter
  • Fang, Kai-Tai

Abstract

Efficient routines for multidimensional numerical integration are provided by quasi-Monte Carlo methods. These methods are based on evaluating the integrand at a set of representative points of the integration area. A set may be called representative if it shows a low discrepancy. However, in dimensions higher than two and for a large number of points the evaluation of discrepancy becomes infeasible. The use of the efficient multiple purpose heuristic Threshold Accepting offers a possibility to obtain at least good approximations to the discrepancy of a given set of points. This paper presents an implementation of Threshold Accepting, an assessment of its performance for some small examples and results for larger sets of points with unknown discrepancy.

Suggested Citation

  • Winker, Peter & Fang, Kai-Tai, 1995. "Application of threshold accepting to the evaluation of the discrepancy of a set of points," Discussion Papers, Series II 248, University of Konstanz, Collaborative Research Centre (SFB) 178 "Internationalization of the Economy".
  • Handle: RePEc:zbw:kondp2:248
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    References listed on IDEAS

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    1. Winker, Peter, 1995. "Identification of multivariate AR-models by threshold accepting," Computational Statistics & Data Analysis, Elsevier, vol. 20(3), pages 295-307, September.
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    Cited by:

    1. Manfred Gilli & Enrico Schumann, 2012. "Heuristic optimisation in financial modelling," Annals of Operations Research, Springer, vol. 193(1), pages 129-158, March.
    2. Lin, D.K.J. & Sharpe, C. & Winker, P., 2010. "Optimized U-type designs on flexible regions," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1505-1515, June.
    3. Lyra, M. & Paha, J. & Paterlini, S. & Winker, P., 2010. "Optimization heuristics for determining internal rating grading scales," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2693-2706, November.
    4. Marianna Lyra & Akwum Onwunta & Peter Winker, 2015. "Threshold accepting for credit risk assessment and validation," Journal of Banking Regulation, Palgrave Macmillan, vol. 16(2), pages 130-145, April.
    5. Winker, Peter, 2005. "The Stochastics of Threshold Accepting: Analysis of an Application to the Uniform Design Problem," Discussion Papers 2005,003E, University of Erfurt, Faculty of Economics, Law and Social Sciences.
    6. Fitzenberger, Bernd & Winker, Peter, 2007. "Improving the computation of censored quantile regressions," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 88-108, September.
    7. Chipman, J. & Winker, P., 2005. "Optimal aggregation of linear time series models," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 311-331, April.
    8. Manfred Gilli & Enrico Schumann, 2009. "Robust regression with optimisation heuristics," Working Papers 011, COMISEF.
    9. Frauke Schleer, 2015. "Finding Starting-Values for the Estimation of Vector STAR Models," Econometrics, MDPI, Open Access Journal, vol. 3(1), pages 1-26, January.
    10. Yong-Dao Zhou & Kai-Tai Fang, 2013. "An efficient method for constructing uniform designs with large size," Computational Statistics, Springer, vol. 28(3), pages 1319-1331, June.
    11. Schleer, Frauke, 2013. "Finding starting-values for maximum likelihood estimation of vector STAR models," ZEW Discussion Papers 13-076, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
    12. Staszewska-Bystrova, Anna & Winker, Peter, 2013. "Constructing narrowest pathwise bootstrap prediction bands using threshold accepting," International Journal of Forecasting, Elsevier, vol. 29(2), pages 221-233.
    13. Manfred GILLI & Peter WINKER, "undated". "A review of heuristic optimization methods in econometrics," Swiss Finance Institute Research Paper Series 08-12, Swiss Finance Institute.
    14. Hellekalek, P., 1998. "Good random number generators are (not so) easy to find," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 46(5), pages 485-505.
    15. Björn Fastrich & Peter Winker, 2012. "Robust portfolio optimization with a hybrid heuristic algorithm," Computational Management Science, Springer, vol. 9(1), pages 63-88, February.

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