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Higher-order approximations to the quantile of the distribution for a class of statistics in the first-order autoregression

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  • Jorge Arevalillo

Abstract

Higher-order approximations for quantiles can be derived upon inversions of the Edgeworth and saddlepoint approximations to the distribution function of a statistic. The inversion of the Edgeworth expansion leads to the well known Cornish–Fisher expansion. This paper deals with the inversions of Esscher’s, Lugannani–Rice and r* saddlepoint approximations for a class of statistics in the first-order autoregression. Such inversions provide analytically explicit approximations to the quantile, alternative to the Cornish–Fisher expansion. We assess the accuracy of the new approximations both theoretically and numerically and compare them with the normal approximation and the second and third-order Cornish–Fisher expansions. Copyright Sociedad de Estadística e Investigación Operativa 2014

Suggested Citation

  • Jorge Arevalillo, 2014. "Higher-order approximations to the quantile of the distribution for a class of statistics in the first-order autoregression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 291-310, June.
    • Handle: RePEc:spr:testjl:v:23:y:2014:i:2:p:291-310
    DOI: 10.1007/s11749-013-0348-0
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    References listed on IDEAS

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    1. Jorge Arevalillo, 2012. "Exploring the relation between the r* approximation and the Edgeworth expansion," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(8), pages 1009-1024, November.
    2. repec:lmu:muenar:20113 is not listed on IDEAS
    3. Broda, Simon & Carstensen, Kai & Paolella, Marc S., 2007. "Bias-adjusted estimation in the ARX(1) model," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3355-3367, April.
    4. Yoshimichi Ochi, 1983. "Asymptotic Expansions For The Distribution Of An Estimator In The First‐Order Autoregressive Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(1), pages 57-67, January.
    5. Wang, Suojin, 1995. "One-step saddlepoint approximations for quantiles," Computational Statistics & Data Analysis, Elsevier, vol. 20(1), pages 65-74, July.
    6. Monti, Anna Clara, 1993. "A new look at the relationship between Edgeworth expansion and saddlepoint approximation," Statistics & Probability Letters, Elsevier, vol. 17(1), pages 49-52, May.
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