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Evaluating Nearly Singular Multinormal Expectations with Application to Wave Distributions

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  • Per A. Brodtkorb

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Abstract

The numerical computation of expectations for (nearly) singular multivariate normal distribution is a difficult problem, which frequently occurs in widely varying statistical contexts. In this article we discuss several strategies to improve the algorithm proposed by Genz and Kwong (2000) when either a moderate accuracy is requested, the correlation structure is strong, and, most importantly, the dimension of the integral is large. Test results for typical problems show an average speedup of 10 using the modified algorithm, but even more is gained as the dimension of the problem increases. We apply the modified algorithm to compute long-run distributions of Gaussian wave characteristics, a difficult problem where previous algorithms fail to compute accurate values in reasonable time.

Suggested Citation

  • Per A. Brodtkorb, 2006. "Evaluating Nearly Singular Multinormal Expectations with Application to Wave Distributions," Methodology and Computing in Applied Probability, Springer, vol. 8(1), pages 65-91, March.
    • Handle: RePEc:spr:metcap:v:8:y:2006:i:1:d:10.1007_s11009-006-7289-y
    DOI: 10.1007/s11009-006-7289-y
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    References listed on IDEAS

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    1. Charles W. Dunnett, 1989. "Multivariate Normal Probability Integrals with Product Correlation Structure," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 38(3), pages 564-579, November.
    2. M. J. R. Healy, 1968. "Algorithm as 6: Triangular Decomposition of a Symmetric Matrix," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 17(2), pages 195-197, June.
    3. 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.
    4. Rychlik, Igor, 1987. "A note on Durbin's formula for the first-passage density," Statistics & Probability Letters, Elsevier, vol. 5(6), pages 425-428, October.
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    Cited by:

    1. Vardar-Acar, Ceren & Bulut, Hatice, 2015. "Bounds on the expected value of maximum loss of fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 117-122.
    2. Andrew M. Ross, 2010. "Computing Bounds on the Expected Maximum of Correlated Normal Variables," Methodology and Computing in Applied Probability, Springer, vol. 12(1), pages 111-138, March.

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