IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v21y2012i4p697-729.html
   My bibliography  Save this article

Estimating an endpoint with high-order moments

Author

Listed:
  • Stéphane Girard
  • Armelle Guillou
  • Gilles Stupfler

Abstract

We present a new method for estimating the endpoint of a unidimensional sample when the distribution function decreases at a polynomial rate to zero in the neighborhood of the endpoint. The estimator is based on the use of high-order moments of the variable of interest. It is assumed that the order of the moments goes to infinity, and we give conditions on its rate of divergence to get the asymptotic normality of the estimator. The good performance of the estimator is illustrated on some finite sample situations. Copyright Sociedad de Estadística e Investigación Operativa 2012

Suggested Citation

  • Stéphane Girard & Armelle Guillou & Gilles Stupfler, 2012. "Estimating an endpoint with high-order moments," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(4), pages 697-729, December.
    • Handle: RePEc:spr:testjl:v:21:y:2012:i:4:p:697-729
    DOI: 10.1007/s11749-011-0277-8
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11749-011-0277-8
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11749-011-0277-8?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. Peter Hall & Julian Z. Wang, 2005. "Bayesian likelihood methods for estimating the end point of a distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 717-729, November.
    2. Neves, Cláudia & Pereira, António, 2010. "Detecting finiteness in the right endpoint of light-tailed distributions," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 437-444, March.
    3. Goldenshluger, A. & Tsybakov, A., 2004. "Estimating the endpoint of a distribution in the presence of additive observation errors," Statistics & Probability Letters, Elsevier, vol. 68(1), pages 39-49, June.
    4. Einmahl, J. H.J. & Dekkers, A. L.M. & de Haan, L., 1989. "A moment estimator for the index of an extreme-value distribution," Other publications TiSEM 81970cb3-5b7a-4cad-9bf6-2, Tilburg University, School of Economics and Management.
    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. Daouia, Abdelaati & Girard, Stéphane & Guillou, Armelle, 2014. "A Γ-moment approach to monotonic boundary estimation," Journal of Econometrics, Elsevier, vol. 178(2), pages 727-740.
    2. Hong-Jiang Wu & Ying-Ying Zhang & Han-Yu Li, 2023. "Expectation identities from integration by parts for univariate continuous random variables with applications to high-order moments," Statistical Papers, Springer, vol. 64(2), pages 477-496, April.
    3. Matheus Henrique Junqueira Saldanha & Adriano Kamimura Suzuki, 2023. "On dealing with the unknown population minimum in parametric inference," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 107(3), pages 509-535, September.

    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. Matheus Henrique Junqueira Saldanha & Adriano Kamimura Suzuki, 2023. "On dealing with the unknown population minimum in parametric inference," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 107(3), pages 509-535, September.
    2. Fátima Brilhante, M. & Ivette Gomes, M. & Pestana, Dinis, 2013. "A simple generalisation of the Hill estimator," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 518-535.
    3. Igor Fedotenkov, 2020. "A Review of More than One Hundred Pareto-Tail Index Estimators," Statistica, Department of Statistics, University of Bologna, vol. 80(3), pages 245-299.
    4. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
    5. Kuosmanen, Timo & Johnson, Andrew, 2017. "Modeling joint production of multiple outputs in StoNED: Directional distance function approach," European Journal of Operational Research, Elsevier, vol. 262(2), pages 792-801.
    6. Gadea Rivas, María Dolores & Olmo, José, 2024. "Testing extreme warming and geographical heterogeneity," UC3M Working papers. Economics 45023, Universidad Carlos III de Madrid. Departamento de Economía.
    7. Phornchanok Cumperayot & Casper G. de Vries, 2006. "Large Swings in Currencies driven by Fundamentals," Tinbergen Institute Discussion Papers 06-086/2, Tinbergen Institute.
    8. Virta, Joni & Lietzén, Niko & Viitasaari, Lauri & Ilmonen, Pauliina, 2024. "Latent model extreme value index estimation," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
    9. Einmahl, J.H.J. & de Haan, L.F.M. & Krajina, A., 2009. "Estimating Extreme Bivariate Quantile Regions," Other publications TiSEM 007ce0a9-dd94-4301-ad62-1, Tilburg University, School of Economics and Management.
    10. Estate Khmaladze & Wolfgang Weil, 2008. "Local empirical processes near boundaries of convex bodies," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(4), pages 813-842, December.
    11. Einmahl, John H.J. & de Haan, Laurens & Sinha, Ashoke Kumar, 1997. "Estimating the spectral measure of an extreme value distribution," Stochastic Processes and their Applications, Elsevier, vol. 70(2), pages 143-171, October.
    12. Xue-Zhong He & Youwei Li, 2017. "The adaptiveness in stock markets: testing the stylized facts in the DAX 30," Journal of Evolutionary Economics, Springer, vol. 27(5), pages 1071-1094, November.
    13. Einmahl, J.H.J. & Li, Jun & Liu, Regina, 2015. "Bridging Centrality and Extremity : Refining Empirical Data Depth using Extreme Value Statistics," Discussion Paper 2015-020, Tilburg University, Center for Economic Research.
    14. Marta Ferreira, 2024. "Extremal index: estimation and resampling," Computational Statistics, Springer, vol. 39(5), pages 2703-2720, July.
    15. Ghosh, Souvik & Resnick, Sidney, 2010. "A discussion on mean excess plots," Stochastic Processes and their Applications, Elsevier, vol. 120(8), pages 1492-1517, August.
    16. Wager, Stefan, 2014. "Subsampling extremes: From block maxima to smooth tail estimation," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 335-353.
    17. de Haan, Laurens & Canto e Castro, Luisa, 2006. "A class of distribution functions with less bias in extreme value estimation," Statistics & Probability Letters, Elsevier, vol. 76(15), pages 1617-1624, September.
    18. Charnchai Leuwattanachotinan & Casper G. de Vries, 2015. "Extreme Linkages in Financial Markets: Macro Shocks and Systemic Risk," PIER Discussion Papers 2, Puey Ungphakorn Institute for Economic Research.
    19. Kneip, Alois & Simar, Léopold & Van Keilegom, Ingrid, 2015. "Frontier estimation in the presence of measurement error with unknown variance," Journal of Econometrics, Elsevier, vol. 184(2), pages 379-393.
    20. Zhu, Sha & Dekker, Rommert & van Jaarsveld, Willem & Renjie, Rex Wang & Koning, Alex J., 2017. "An improved method for forecasting spare parts demand using extreme value theory," European Journal of Operational Research, Elsevier, vol. 261(1), pages 169-181.

    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:21:y:2012:i:4:p:697-729. 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.