Methodology and Computing in Applied Probability

, Volume 18, Issue 3, pp 911–920 | Cite as

Expansions for Log Densities of Multivariate Estimates

  • Christopher S. Withers
  • Saralees NadarajahEmail author


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


Bell polynomials Multivariate normal distribution Normal distribution 

Mathematics Subject Classification (2010)



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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Industrial Research LimitedLower HuttNew Zealand
  2. 2.University of ManchesterManchesterUK

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