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Expansions for Log Densities of Multivariate Estimates

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  • Christopher S. Withers

    (Industrial Research Limited)

  • Saralees Nadarajah

    (University of Manchester)

Abstract

Withers and Nadarajah (Stat Pap 51:247–257; 2010) gave simple Edgeworth-type expansions for log densities of univariate estimates whose cumulants satisfy standard expansions. Here, we extend the Edgeworth-type expansions for multivariate estimates with coefficients expressed in terms of Bell polynomials. Their advantage over the usual Edgeworth expansion for the density is that the kth term is a polynomial of degree only k + 2, not 3k. Their advantage over those in Takemura and Takeuchi [Sankhyā, A, 50, 1998, 111-136] is computational efficiency

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:18:y:2016:i:3:d:10.1007_s11009-016-9488-5
    DOI: 10.1007/s11009-016-9488-5
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    References listed on IDEAS

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    1. Withers, Christopher S. & Nadarajah, Saralees, 2014. "The dual multivariate Charlier and Edgeworth expansions," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 76-85.
    2. Withers, C. S., 2000. "A simple expression for the multivariate Hermite polynomials," Statistics & Probability Letters, Elsevier, vol. 47(2), pages 165-169, April.
    3. Christopher Withers & Saralees Nadarajah, 2010. "Expansions for log densities of asymptotically normal estimates," Statistical Papers, Springer, vol. 51(2), pages 247-257, June.
    4. Kim, Hyoung-Moon & Genton, Marc G., 2011. "Characteristic functions of scale mixtures of multivariate skew-normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 102(7), pages 1105-1117, August.
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