Cornish-Fisher expansions using sample cumulants and monotonic transformations
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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Volume (Year): 103 (2012)
Issue (Month): 1 (January)
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- Yoshihiko Maesono, 1998. "Asymptotic Comparisons of Several Variance Estimators and their Effects for Studentizations," Annals of the Institute of Statistical Mathematics, Springer, vol. 50(3), pages 451-470, September.
- Ogasawara, Haruhiko, 2009. "Asymptotic expansions in mean and covariance structure analysis," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 902-912, May.
- Robert Boik, 2008. "Accurate confidence intervals in regression analyses of non-normal data," Annals of the Institute of Statistical Mathematics, Springer, vol. 60(1), pages 61-83, March.
- Ogasawara, Haruhiko, 2010. "Asymptotic expansions for the pivots using log-likelihood derivatives with an application in item response theory," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2149-2167, October.
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