Cornish-Fisher expansions using sample cumulants and monotonic transformations

Haruhiko Ogasawara

Journal of Multivariate Analysis, 2012, vol. 103, issue 1, 1-18

Abstract: General formulas of the asymptotic cumulants of a studentized parameter estimator are given up to the fourth order with the added higher-order asymptotic variance. Using the sample counterparts of the asymptotic cumulants, formulas for the Cornish-Fisher expansions with third-order accuracy are obtained. Some new methods of monotonic transformations of the studentized estimator are presented. In addition, similar transformations of a fixed normal deviate are proposed up to the same order with some asymptotic comparisons to the transformations of the studentized estimator. Applications to a mean and a binomial proportion are shown with simulations for estimation of the proportion.

Keywords: Asymptotic; expansions; Cornish-Fisher; expansion; Studentization; Monotonic; transformation; Asymptotic; cumulants (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (6)

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