Expansions for Log Densities of Multivariate Estimates

Christopher S. Withers () and Saralees Nadarajah ()
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Christopher S. Withers: Industrial Research Limited
Saralees Nadarajah: University of Manchester

Methodology and Computing in Applied Probability, 2016, vol. 18, issue 3, 911-920

Abstract: 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

Keywords: Bell polynomials; Multivariate normal distribution; Normal distribution; 62E20 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s11009-016-9488-5

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