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A simple expression for the multivariate Hermite polynomials

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  • 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
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    Citations

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    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.

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