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Error bounds for asymptotic expansion of the scale mixtures of the normal distribution

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Summary

LetX be a standard normal random variable and let σ be a positive random variable independent ofX. The distribution of η=σX is expanded around that ofN(0, 1) and its error bounds are obtained. Bounds are given in terms of E(σ2V−σ2−1)k whereσ2Vσ−2 denotes the maximum of the two quantitiesσ2 andσ−2, andk is a positive integer, and of E(σ2−1)k, ifk is even.

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Authors
  1. Ryoichi Shimizu
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The Institute of Statistical Mathematics

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Shimizu, R. Error bounds for asymptotic expansion of the scale mixtures of the normal distribution. Ann Inst Stat Math 39, 611–622 (1987). https://doi.org/10.1007/BF02491493

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  • DOI: https://doi.org/10.1007/BF02491493

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