Publication:
Higher order relations between Cornish-Fisher expansions and inversions of saddlepoint approximations

dc.contributor.author Maesono, Y en_US
dc.contributor.author Penev, Spiridon en_US
dc.date.accessioned 2021-11-25T13:41:01Z
dc.date.available 2021-11-25T13:41:01Z
dc.date.issued 1998 en_US
dc.description.abstract 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. en_US
dc.identifier.issn 0389-5602 en_US
dc.identifier.uri http://hdl.handle.net/1959.4/40272
dc.language English
dc.language.iso EN en_US
dc.rights CC BY-NC-ND 3.0 en_US
dc.rights.uri https://creativecommons.org/licenses/by-nc-nd/3.0/au/ en_US
dc.source Legacy MARC en_US
dc.title Higher order relations between Cornish-Fisher expansions and inversions of saddlepoint approximations en_US
dc.type Journal Article en
dcterms.accessRights metadata only access
dspace.entity.type Publication en_US
unsw.accessRights.uri http://purl.org/coar/access_right/c_14cb
unsw.description.notePublic Original inactive link: http://www.journalarchive.jst.go.jp/english/jnlabstract_en.php?cdjournal=jjss1995&cdvol=28&noissue=1&startpage=21 en_US
unsw.relation.faculty Science
unsw.relation.ispartofissue 1 en_US
unsw.relation.ispartofjournal Journal of the Japan statistical society en_US
unsw.relation.ispartofpagefrompageto 21-38 en_US
unsw.relation.ispartofvolume 28 en_US
unsw.relation.originalPublicationAffiliation Maesono, Y en_US
unsw.relation.originalPublicationAffiliation Penev, Spiridon, Mathematics & Statistics, Faculty of Science, UNSW en_US
unsw.relation.school School of Mathematics & Statistics *
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