Journal
JOURNAL OF MULTIVARIATE ANALYSIS
Volume 103, Issue 1, Pages 1-18Publisher
ELSEVIER INC
DOI: 10.1016/j.jmva.2011.05.013
Keywords
Asymptotic expansions; Cornish-Fisher expansion; Studentization; Monotonic transformation; Asymptotic cumulants
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Funding
- Japanese Ministry of Education, Culture, Sports, Science and Technology [23500341]
- Grants-in-Aid for Scientific Research [23500341] Funding Source: KAKEN
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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. (C) 2011 Elsevier Inc. All rights reserved.
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