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Tilted Edgeworth expansions for asymptotically normal vectors

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Abstract

We obtain the Edgeworth expansion for \({P(n^{1/2}(\hat{\theta}-\theta) < x)}\) and its derivatives, and the tilted Edgeworth (or saddlepoint or small sample) expansion for \({P(\hat{\theta} < x)}\) and its derivatives where \({\hat{\theta}}\) is any vector estimate having the standard cumulant expansions in powers of \({n^{-1}}\) .

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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, M13 9PL, 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. Tilted Edgeworth expansions for asymptotically normal vectors. Ann Inst Stat Math 62, 1113–1142 (2010). https://doi.org/10.1007/s10463-008-0206-0

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  • DOI: https://doi.org/10.1007/s10463-008-0206-0

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