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Expansions for log densities of asymptotically normal estimates

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Abstract

Edgeworth–type expansions are given for the log density and also for the derivatives of the density of an asymptotically normal random variable having the standard expansions for its cumulants. Expansions for the log density are much simpler than for the density. In fact the rth term of the expansion for the log density is a polynomial of degree only r + 2, while that for the density is a polynomial of degree 3r.

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Authors and Affiliations

  1. Applied Mathematics Group, Industrial Research Limited, Lower Hutt, New Zealand

    Christopher S. Withers

  2. School of Mathematics, University of Manchester, Manchester, M60 1QD, UK

    Saralees Nadarajah

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  1. Christopher S. Withers
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  2. Saralees Nadarajah
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Correspondence to Saralees Nadarajah.

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Withers, C.S., Nadarajah, S. Expansions for log densities of asymptotically normal estimates. Stat Papers 51, 247–257 (2010). https://doi.org/10.1007/s00362-008-0135-2

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  • DOI: https://doi.org/10.1007/s00362-008-0135-2

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