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Expansions about the Gamma for the Distribution and Quantiles of a Standard Estimate

Author

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  • Christopher S. Withers

    (Industrial Research Limited)

  • Saralees Nadarajah

    (University of Manchester)

Abstract

We give expansions for the distribution, density, and quantiles of an estimate, building on results of Cornish, Fisher, Hill, Davis and the authors. The estimate is assumed to be non-lattice with the standard expansions for its cumulants. By expanding about a skew variable with matched skewness, one can drastically reduce the number of terms needed for a given level of accuracy. The building blocks generalize the Hermite polynomials. We demonstrate with expansions about the gamma.

Suggested Citation

  • Christopher S. Withers & Saralees Nadarajah, 2014. "Expansions about the Gamma for the Distribution and Quantiles of a Standard Estimate," Methodology and Computing in Applied Probability, Springer, vol. 16(3), pages 693-713, September.
    • Handle: RePEc:spr:metcap:v:16:y:2014:i:3:d:10.1007_s11009-013-9328-9
    DOI: 10.1007/s11009-013-9328-9
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    References listed on IDEAS

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    1. Zhang, Lan & Mykland, Per A. & Aït-Sahalia, Yacine, 2011. "Edgeworth expansions for realized volatility and related estimators," Journal of Econometrics, Elsevier, vol. 160(1), pages 190-203, January.
    2. Withers, C. S., 2000. "A simple expression for the multivariate Hermite polynomials," Statistics & Probability Letters, Elsevier, vol. 47(2), pages 165-169, April.
    3. C. Withers, 1988. "Nonparametric confidence intervals for functions of several distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 40(4), pages 727-746, December.
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    Cited by:

    1. C. S. Withers, 2024. "5th-Order Multivariate Edgeworth Expansions for Parametric Estimates," Mathematics, MDPI, vol. 12(6), pages 1-28, March.

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