IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v47y2000i2p165-169.html
   My bibliography  Save this article

A simple expression for the multivariate Hermite polynomials

Author

Listed:
  • Withers, C. S.

Abstract

We give a simple method for obtaining the multivariate Hermite polynomials. Explicitly we give all of them up to order three: these are needed for the second-order Edgeworth expansions for the distribution and density of most standardised vector estimates.

Suggested Citation

  • Withers, C. S., 2000. "A simple expression for the multivariate Hermite polynomials," Statistics & Probability Letters, Elsevier, vol. 47(2), pages 165-169, April.
    • Handle: RePEc:eee:stapro:v:47:y:2000:i:2:p:165-169
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(99)00153-4
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Withers, Christopher S. & Nadarajah, Saralees, 2010. "Some conditional expectation identities for the multivariate normal," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2250-2253, October.
    2. Withers, C.S. & McGavin, P.N., 2006. "Expressions for the normal distribution and repeated normal integrals," Statistics & Probability Letters, Elsevier, vol. 76(5), pages 479-487, March.
    3. Christopher S. Withers & Saralees Nadarajah, 2011. "New Expressions for Repeated Upper Tail Integrals of the Normal Distribution," Methodology and Computing in Applied Probability, Springer, vol. 13(4), pages 855-871, December.
    4. Seungmoon Choi, 2011. "Closed-Form Likelihood Expansions for Multivariate Time-Inhomogeneous Diffusions," School of Economics and Public Policy Working Papers 2011-26, University of Adelaide, School of Economics and Public Policy.
    5. Andrew Papanicolaou, 2018. "Consistent Time-Homogeneous Modeling of SPX and VIX Derivatives," Papers 1812.05859, arXiv.org, revised Mar 2022.
    6. Choi, Seungmoon, 2013. "Closed-form likelihood expansions for multivariate time-inhomogeneous diffusions," Journal of Econometrics, Elsevier, vol. 174(2), pages 45-65.
    7. Christopher S. Withers & Saralees Nadarajah, 2014. "Expansions about the Gamma for the Distribution and Quantiles of a Standard Estimate," Methodology and Computing in Applied Probability, Springer, vol. 16(3), pages 693-713, September.
    8. Withers, Christopher S. & Nadarajah, Saralees, 2010. "Expansions for the multivariate normal," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1311-1316, May.
    9. Withers, Christopher S. & Nadarajah, Saralees, 2013. "The distribution of the amplitude and phase of the mean of a sample of complex random variables," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 128-152.
    10. Withers, Christopher S. & Nadarajah, Saralees, 2009. "Accurate tests and intervals based on linear cusum statistics," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 689-697, March.
    11. Christopher S. Withers & Saralees Nadarajah, 2016. "Expansions for Log Densities of Multivariate Estimates," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 911-920, September.
    12. Withers, Christopher S. & Nadarajah, Saralees, 2014. "The dual multivariate Charlier and Edgeworth expansions," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 76-85.
    13. Sun, Ping, 2007. "Moment representation of Bernoulli polynomial, Euler polynomial and Gegenbauer polynomials," Statistics & Probability Letters, Elsevier, vol. 77(7), pages 748-751, April.
    14. Yacine Ait-Sahalia, 2002. "Closed-Form Likelihood Expansions for Multivariate Diffusions," NBER Working Papers 8956, National Bureau of Economic Research, Inc.
    15. Willink, R., 2005. "Normal moments and Hermite polynomials," Statistics & Probability Letters, Elsevier, vol. 73(3), pages 271-275, July.
    16. Jiang, Chen & Vega, Manuel A. & Todd, Michael D. & Hu, Zhen, 2022. "Model correction and updating of a stochastic degradation model for failure prognostics of miter gates," Reliability Engineering and System Safety, Elsevier, vol. 218(PA).
    17. Andrew Papanicolaou, 2022. "Consistent time‐homogeneous modeling of SPX and VIX derivatives," Mathematical Finance, Wiley Blackwell, vol. 32(3), pages 907-940, July.
    18. Gnameho Kossi & Stadje Mitja & Pelsser Antoon, 2024. "A gradient method for high-dimensional BSDEs," Monte Carlo Methods and Applications, De Gruyter, vol. 30(2), pages 183-203.

    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:eee:stapro:v:47:y:2000:i:2:p:165-169. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.