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Fast computation of high-dimensional multivariate normal probabilities

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  • Phinikettos, Ioannis
  • Gandy, Axel

Abstract

A new efficient method is proposed to compute multivariate normal probabilities over rectangles in high dimensions. The method exploits four variance reduction techniques: conditional Monte Carlo, importance sampling, splitting and control variates. Simulation results are presented that evaluate the performance of the new proposed method. The new method is designed for computing small exceedance probabilities.

Suggested Citation

  • Phinikettos, Ioannis & Gandy, Axel, 2011. "Fast computation of high-dimensional multivariate normal probabilities," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1521-1529, April.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:4:p:1521-1529
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    References listed on IDEAS

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    1. Tamás Szántai, 2000. "Improved Bounds and Simulation Procedures on the Value of the Multivariate Normal Probability Distribution Function," Annals of Operations Research, Springer, vol. 100(1), pages 85-101, December.
    2. Mark J. Schervish, 1984. "Multivariate Normal Probabilities with Error Bound," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 33(1), pages 81-94, March.
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    4. D. Y. Lin & L. J. Wei & Z. Ying, 2002. "Model-Checking Techniques Based on Cumulative Residuals," Biometrics, The International Biometric Society, vol. 58(1), pages 1-12, March.
    5. Sandor, Zsolt & Andras, P.Peter, 2004. "Alternative sampling methods for estimating multivariate normal probabilities," Journal of Econometrics, Elsevier, vol. 120(2), pages 207-234, June.
    6. Vijverberg, Wim P. M., 1997. "Monte Carlo evaluation of multivariate normal probabilities," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 281-307.
    7. Tetsuhisa Miwa & A. J. Hayter & Satoshi Kuriki, 2003. "The evaluation of general non‐centred orthant probabilities," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 223-234, February.
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    Cited by:

    1. Shuang Zhu & R. Pace, 2014. "Modeling Spatially Interdependent Mortgage Decisions," The Journal of Real Estate Finance and Economics, Springer, vol. 49(4), pages 598-620, November.

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