HIGHER ORDER RELATIONS BETWEEN CORNISH-FISHER EXPANSIONS AND INVERSIONS OF SADDLEPOINT APPROXIMATIONS
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- Maesono Yoshihiko
- Faculty of Economics, Kyushu University
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- Penev Spiridon I.
- Department of Statistics, The University of New South Wales
説明
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.
収録刊行物
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- ＪＯＵＲＮＡＬ ＯＦ ＴＨＥ ＪＡＰＡＮ ＳＴＡＴＩＳＴＩＣＡＬ ＳＯＣＩＥＴＹ
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ＪＯＵＲＮＡＬ ＯＦ ＴＨＥ ＪＡＰＡＮ ＳＴＡＴＩＳＴＩＣＡＬ ＳＯＣＩＥＴＹ 28 (1), 21-38, 1998
日本統計学会
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キーワード
詳細情報 詳細情報について
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- CRID
- 1390001205285957632
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- NII論文ID
- 130003582679
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- ISSN
- 13486365
- 18822754
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- HANDLE
- 1959.4/40272
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- 本文言語コード
- en
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- データソース種別
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- JaLC
- Crossref
- CiNii Articles
- OpenAIRE
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- 抄録ライセンスフラグ
- 使用不可
