Cornish-Fisher expansions using sample cumulants and monotonic transformations |
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Authors: | Haruhiko Ogasawara |
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Affiliation: | Department of Information and Management Science, Otaru University of Commerce, 3-5-21, Midori, Otaru 047-8501, Japan |
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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. |
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Keywords: | primary, 62 E20 secondary, 62H10 |
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