IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v23y2014i2p291-310.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11749-013-0348-0
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11749-013-0348-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. Wang, Suojin, 1995. "One-step saddlepoint approximations for quantiles," Computational Statistics & Data Analysis, Elsevier, vol. 20(1), pages 65-74, July.
    5. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Arevalillo, Jorge M, 2024. "On the empirical approximation to quantiles from Lugannani–Rice saddlepoint formula," Statistics & Probability Letters, Elsevier, vol. 209(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Arevalillo, Jorge M, 2024. "On the empirical approximation to quantiles from Lugannani–Rice saddlepoint formula," Statistics & Probability Letters, Elsevier, vol. 209(C).
    2. 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.
    3. Broda, S. & Paolella, M.S., 2009. "Evaluating the density of ratios of noncentral quadratic forms in normal variables," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1264-1270, February.
    4. Marsh, Patrick, 2001. "Edgeworth expansions in Gaussian autoregression," Statistics & Probability Letters, Elsevier, vol. 54(3), pages 233-241, October.
    5. Gatto, Riccardo, 2008. "A saddlepoint approximation to the probability of ruin in the compound Poisson process with diffusion," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1948-1954, September.
    6. Kakizawa, Yoshihide, 1998. "On exponential rates of estimators of the parameter in the first-order autoregressive process," Statistics & Probability Letters, Elsevier, vol. 38(4), pages 355-362, July.
    7. Kiviet, Jan F. & Phillips, Garry D.A., 2012. "Higher-order asymptotic expansions of the least-squares estimation bias in first-order dynamic regression models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3705-3729.
    8. Ronald W. Butler & Marc S. Paolella, 2017. "Autoregressive Lag—Order Selection Using Conditional Saddlepoint Approximations," Econometrics, MDPI, vol. 5(3), pages 1-33, September.
    9. Dominique Guegan & Bertrand K. Hassani & Kehan Li, 2016. "A robust confidence interval of historical Value-at-Risk for small sample," Documents de travail du Centre d'Economie de la Sorbonne 16034, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    10. Riccardo Gatto, 2019. "Saddlepoint Approximation for Data in Simplices: A Review with New Applications," Stats, MDPI, vol. 2(1), pages 1-27, February.
    11. Dominique Guegan & Bertrand Hassani & Kehan Li, 2017. "Measuring risks in the extreme tail: The extreme VaR and its confidence interval," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01317391, HAL.
    12. van Giersbergen, Noud P.A., 2016. "The ability to correct the bias in the stable AD(1,1) model with a feedback effect," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 186-204.
    13. Gatto, Riccardo & Jammalamadaka, S. Rao, 2002. "A saddlepoint approximation for testing exponentiality against some increasing failure rate alternatives," Statistics & Probability Letters, Elsevier, vol. 58(1), pages 71-81, May.
    14. Christopher Withers & Saralees Nadarajah, 2010. "Tilted Edgeworth expansions for asymptotically normal vectors," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(6), pages 1113-1142, December.
    15. Riccardo Gatto, 2012. "Saddlepoint Approximations to Tail Probabilities and Quantiles of Inhomogeneous Discounted Compound Poisson Processes with Periodic Intensity Functions," Methodology and Computing in Applied Probability, Springer, vol. 14(4), pages 1053-1074, December.
    16. Riccardo Gatto & Benjamin Baumgartner, 2014. "Value at Ruin and Tail Value at Ruin of the Compound Poisson Process with Diffusion and Efficient Computational Methods," Methodology and Computing in Applied Probability, Springer, vol. 16(3), pages 561-582, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:testjl:v:23:y:2014:i:2:p:291-310. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.