HIGHER ORDER RELATIONS BETWEEN CORNISH-FISHER EXPANSIONS AND INVERSIONS OF SADDLEPOINT APPROXIMATIONS

DOI HANDLE 10 References Open Access

Description

Many numerical examples have demonstrated that the saddlepoint approximation for the cumulative distribution function of a general normalised statistic behaves better in comparison with the third order Edgeworth expansion. This effect is especially pronounced in the tails. Here we are dealing with the inverse problem of quantile evaluation. The inversion of the Lugannani-Rice approximation is compared with the Cornish-Fisher expansion both theoretically and numerically. We show in a very general setting that the expansion of the inversion of the Lugannani-Rice approximation up to third order coincides with the Cornish-Fisher expansion. Based on this, an explanation of the superiority of the former in comparison with the latter in the tails and for small samples is given. An explicit approximation of the inversion of the Lugannani-Rice formula is suggested that utilizes the information in the cumulant generating function and improves upon the Cornish-Fisher formula.

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Details 詳細情報について

  • CRID
    1390001205285957632
  • NII Article ID
    130003582679
  • DOI
    10.14490/jjss1995.28.21
  • ISSN
    13486365
    18822754
  • HANDLE
    1959.4/40272
  • Text Lang
    en
  • Data Source
    • JaLC
    • Crossref
    • CiNii Articles
    • OpenAIRE
  • Abstract License Flag
    Disallowed

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