IDEAS home Printed from https://ideas.repec.org/a/inm/orijoc/v32y2020i1p164-171.html
   My bibliography  Save this article

Recursive Calculation Model for a Special Multivariate Normal Probability of First-Order Stationary Sequence

Author

Listed:
  • Jietao Xie

    (Baicheng Ordnance Test Center of China, Baicheng 137001, Jilin, China)

  • Juan Wu

    (Baicheng Ordnance Test Center of China, Baicheng 137001, Jilin, China)

Abstract

The consecutive hit probability of antiaircraft artillery corresponds to the multivariate normal probability distribution. The computational complexity depends on the length of the firing error sequence (i.e., the integral dimension may exceed 100). The traditional numerical integration and the Monte Carlo method are too slow for this calculation. This paper established the state equation of the firing error sequence, which was the bridge between the multivariate normal probability distribution and stochastic process theory. The recursive calculation model was given after the rigorous derivation process. The accuracy and computational complexity of the model were quantified by theoretical analysis and expressed intuitively by examples. The model shows the upper bound for the absolute error, and the computational efficiency is significantly improved.

Suggested Citation

  • Jietao Xie & Juan Wu, 2020. "Recursive Calculation Model for a Special Multivariate Normal Probability of First-Order Stationary Sequence," INFORMS Journal on Computing, INFORMS, vol. 32(1), pages 164-171, January.
  • Handle: RePEc:inm:orijoc:v:32:y:2020:i:1:p:164-171
    DOI: 10.1287/ijoc.2018.0852
    as

    Download full text from publisher

    File URL: https://doi.org/10.1287/ijoc.2018.0852
    Download Restriction: no

    File URL: https://libkey.io/10.1287/ijoc.2018.0852?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. McFadden, Daniel, 1989. "A Method of Simulated Moments for Estimation of Discrete Response Models without Numerical Integration," Econometrica, Econometric Society, vol. 57(5), pages 995-1026, September.
    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.
    3. Peter Craig, 2008. "A new reconstruction of multivariate normal orthant probabilities," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 227-243, February.
    4. 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.
    5. Hajivassiliou, Vassilis & McFadden, Daniel & Ruud, Paul, 1996. "Simulation of multivariate normal rectangle probabilities and their derivatives theoretical and computational results," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 85-134.
    6. Vijverberg, Wim P. M., 1997. "Monte Carlo evaluation of multivariate normal probabilities," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 281-307.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Z. I. Botev, 2017. "The normal law under linear restrictions: simulation and estimation via minimax tilting," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 125-148, January.
    2. 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.
    3. Sándor, Z. & András, P., 2003. "Alternate Samplingmethods for Estimating Multivariate Normal Probabilities," Econometric Institute Research Papers EI 2003-05, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    4. Jacques Huguenin & Florian Pelgrin & Alberto Holly, 2009. "Estimation of multivariate probit models by exact maximum likelihood," Working Papers 0902, University of Lausanne, Institute of Health Economics and Management (IEMS).
    5. 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.
    6. Lee, Lung-fei, 1999. "Estimation of dynamic and ARCH Tobit models," Journal of Econometrics, Elsevier, vol. 92(2), pages 355-390, October.
    7. Andreas Ziegler, 2007. "Simulated classical tests in multinomial probit models," Statistical Papers, Springer, vol. 48(4), pages 655-681, October.
    8. Ziegler Andreas, 2010. "Z-Tests in Multinomial Probit Models under Simulated Maximum Likelihood Estimation: Some Small Sample Properties," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 230(5), pages 630-652, October.
    9. Yannis M. Ioannides & Vassilis A. Hajivassiliou, 2007. "Unemployment and liquidity constraints," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(3), pages 479-510.
    10. Ziegler, Andreas, 2002. "Simulated Classical Tests in the Multiperiod Multinomial Probit Model," ZEW Discussion Papers 02-38, ZEW - Leibniz Centre for European Economic Research.
    11. Geweke, John F. & Keane, Michael P. & Runkle, David E., 1997. "Statistical inference in the multinomial multiperiod probit model," Journal of Econometrics, Elsevier, vol. 80(1), pages 125-165, September.
    12. Maruyama, Shiko, 2014. "Estimation of finite sequential games," Journal of Econometrics, Elsevier, vol. 178(2), pages 716-726.
    13. Michael Scheidler & Reinhard Hujer & Joachim Grammig, 2005. "Discrete choice modelling in airline network management," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(4), pages 467-486.
    14. Ziegler, Andreas, 2001. "Simulated z-tests in multinomial probit models," ZEW Discussion Papers 01-53, ZEW - Leibniz Centre for European Economic Research.
    15. Lee, Lung-Fei, 1997. "Simulated maximum likelihood estimation of dynamic discrete choice statistical models some Monte Carlo results," Journal of Econometrics, Elsevier, vol. 82(1), pages 1-35.
    16. Zsolt Sandor, 2009. "Multinomial discrete choice models (in Russian)," Quantile, Quantile, issue 7, pages 9-19, September.
    17. Daniel Ackerberg, 2009. "A new use of importance sampling to reduce computational burden in simulation estimation," Quantitative Marketing and Economics (QME), Springer, vol. 7(4), pages 343-376, December.
    18. Bryan S. Graham & Andrin Pelican, 2023. "Scenario sampling for large supermodular games," CeMMAP working papers 15/23, Institute for Fiscal Studies.
    19. Rennings, Klaus & Ziegler, Andreas & Zwick, Thomas, 2001. "Employment changes in environmentally innovative firms," ZEW Discussion Papers 01-46, ZEW - Leibniz Centre for European Economic Research.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:orijoc:v:32:y:2020:i:1:p:164-171. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.