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Cornish-Fisher expansions using sample cumulants and monotonic transformations

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  • Ogasawara, Haruhiko

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.

Suggested Citation

  • Ogasawara, Haruhiko, 2012. "Cornish-Fisher expansions using sample cumulants and monotonic transformations," Journal of Multivariate Analysis, Elsevier, vol. 103(1), pages 1-18, January.
  • Handle: RePEc:eee:jmvana:v:103:y:2012:i:1:p:1-18
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    References listed on IDEAS

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    1. Ogasawara, Haruhiko, 2009. "Asymptotic expansions in mean and covariance structure analysis," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 902-912, May.
    2. Yoshihiko Maesono, 1998. "Asymptotic Comparisons of Several Variance Estimators and their Effects for Studentizations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(3), pages 451-470, September.
    3. 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.
    4. Robert Boik, 2008. "Accurate confidence intervals in regression analyses of non-normal data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(1), pages 61-83, March.
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    Cited by:

    1. Haruhiko Ogasawara, 2013. "Asymptotic properties of the Bayes modal estimators of item parameters in item response theory," Computational Statistics, Springer, vol. 28(6), pages 2559-2583, December.
    2. Ogasawara, Haruhiko, 2016. "Asymptotic expansions for the estimators of Lagrange multipliers and associated parameters by the maximum likelihood and weighted score methods," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 20-37.
    3. Ogasawara, Haruhiko, 2013. "Asymptotic cumulants of ability estimators using fallible item parameters," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 144-162.
    4. Ogasawara, Haruhiko, 2015. "Asymptotic cumulants of some information criteria (2nd version)," ビジネス創造センターディスカッション・ペーパー (Discussion papers of the Center for Business Creation) 10252/5497, Otaru University of Commerce.

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