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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.

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  • 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, 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.
    2. 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.
    3. Ogasawara, Haruhiko, 2009. "Asymptotic expansions in mean and covariance structure analysis," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 902-912, May.
    4. 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.
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    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, 2013. "Asymptotic cumulants of ability estimators using fallible item parameters," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 144-162.
    3. Haruhiko Ogasawara, 2021. "A Unified Treatment of Agreement Coefficients and their Asymptotic Results: the Formula of the Weighted Mean of Weighted Ratios," Journal of Classification, Springer;The Classification Society, vol. 38(2), pages 390-422, July.
    4. Marcin Dec, 2019. "From point through density valuation to individual risk assessment in the discounted cash flows method," GRAPE Working Papers 35, GRAPE Group for Research in Applied Economics.
    5. 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.
    6. 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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