IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v82y2012i5p949-958.html
   My bibliography  Save this article

On tail index estimation using a sample with missing observations

Author

Listed:
  • Ilić, Ivana

Abstract

For the sequence of heavy-tailed, dependent and heterogeneous random variables with the missing observations the estimation of the tail-index is considered. Under minimal but verifiable assumption of “extremal dependence” we proved the consistency of a geometric-type estimator (Brito and Freitas, 2003). We extended results from Mladenović and Piterbarg (2008) and proved the consistency and the asymptotic normality of the Hill estimator. Illustrative examples are provided.

Suggested Citation

  • Ilić, Ivana, 2012. "On tail index estimation using a sample with missing observations," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 949-958.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:5:p:949-958
    DOI: 10.1016/j.spl.2012.01.014
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715212000247
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2012.01.014?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. Patrick Kline & Andres Santos, 2013. "Sensitivity to missing data assumptions: Theory and an evaluation of the U.S. wage structure," Quantitative Economics, Econometric Society, vol. 4(2), pages 231-267, July.
    2. Brito, Margarida & Moreira Freitas, Ana Cristina, 2003. "Limiting behaviour of a geometric-type estimator for tail indices," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 211-226, October.
    3. Mladenovic, Zorica & Petrovic, Pavle, 2010. "Cagan's paradox and money demand in hyperinflation: Revisited at daily frequency," Journal of International Money and Finance, Elsevier, vol. 29(7), pages 1369-1384, November.
    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.
    5. Hill, Jonathan B., 2011. "Tail And Nontail Memory With Applications To Extreme Value And Robust Statistics," Econometric Theory, Cambridge University Press, vol. 27(4), pages 844-884, August.
    6. Schultze J. & Steinebach J., 1996. "On Least Squares Estimates Of An Exponential Tail Coefficient," Statistics & Risk Modeling, De Gruyter, vol. 14(4), pages 353-372, April.
    7. Jonathan B. Hill, 2005. "On Tail Index Estimation for Dependent, Heterogenous Data," Econometrics 0505005, University Library of Munich, Germany, revised 24 Mar 2006.
    8. Mladenovic, Pavle & Piterbarg, Vladimir, 2008. "On estimation of the exponent of regular variation using a sample with missing observations," Statistics & Probability Letters, Elsevier, vol. 78(4), pages 327-335, March.
    9. Davidson, James, 2004. "Moment and Memory Properties of Linear Conditional Heteroscedasticity Models, and a New Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 22(1), pages 16-29, January.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. David Anthoff & Richard S. J. Tol, 2022. "Testing the Dismal Theorem," Journal of the Association of Environmental and Resource Economists, University of Chicago Press, vol. 9(5), pages 885-920.
    3. Brito, Margarida & Freitas, Ana Cristina Moreira, 2010. "Consistent estimation of the tail index for dependent data," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1835-1843, December.
    4. Brito, Margarida & Freitas, Ana Cristina Moreira, 2008. "Edgeworth expansion for an estimator of the adjustment coefficient," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 203-208, October.
    5. Christian Schluter, 2018. "Top Incomes, Heavy Tails, and Rank-Size Regressions," Econometrics, MDPI, vol. 6(1), pages 1-16, March.
    6. Iglesias, Emma M. & Linton, Oliver, 2009. "Estimation of tail thickness parameters from GJR-GARCH models," UC3M Working papers. Economics we094726, Universidad Carlos III de Madrid. Departamento de Economía.
    7. Christian Schluter, 2021. "On Zipf’s law and the bias of Zipf regressions," Empirical Economics, Springer, vol. 61(2), pages 529-548, August.
    8. Brito, Margarida & Moreira Freitas, Ana Cristina, 2006. "Weak convergence of a bootstrap geometric-type estimator with applications to risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 571-584, June.
    9. Li, Youwei & Hamill, Philip A. & Opong, Kwaku K., 2010. "Do benchmark African equity indices exhibit the stylized facts?," Global Finance Journal, Elsevier, vol. 21(1), pages 71-97.
    10. Demiralay, Sercan & Ulusoy, Veysel, 2014. "Value-at-risk Predictions of Precious Metals with Long Memory Volatility Models," MPRA Paper 53229, University Library of Munich, Germany.
    11. 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.
    12. Lombardi, Marco J. & Calzolari, Giorgio, 2009. "Indirect estimation of [alpha]-stable stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2298-2308, April.
    13. 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.
    14. Victor Chernozhukov & Iván Fernández‐Val & Blaise Melly, 2013. "Inference on Counterfactual Distributions," Econometrica, Econometric Society, vol. 81(6), pages 2205-2268, November.
    15. Manuel Arellano & Stéphane Bonhomme, 2017. "Quantile Selection Models With an Application to Understanding Changes in Wage Inequality," Econometrica, Econometric Society, vol. 85, pages 1-28, January.
    16. Shao, Xiaofeng, 2011. "A bootstrap-assisted spectral test of white noise under unknown dependence," Journal of Econometrics, Elsevier, vol. 162(2), pages 213-224, June.
    17. Davidson James & Rambaccussing Dooruj, 2015. "A Test of the Long Memory Hypothesis Based on Self-Similarity," Journal of Time Series Econometrics, De Gruyter, vol. 7(2), pages 115-141, July.
    18. Mohamed Chikhi & Anne Péguin-Feissolle & Michel Terraza, 2013. "SEMIFARMA-HYGARCH Modeling of Dow Jones Return Persistence," Computational Economics, Springer;Society for Computational Economics, vol. 41(2), pages 249-265, February.
    19. Raj Chetty & Nathaniel Hendren & Patrick Kline & Emmanuel Saez, 2014. "Where is the land of Opportunity? The Geography of Intergenerational Mobility in the United States," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 129(4), pages 1553-1623.
    20. CHIA-LIN CHANG & MICHAEL McALEER & ROENGCHAI TANSUCHAT, 2012. "Modelling Long Memory Volatility In Agricultural Commodity Futures Returns," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 7(02), pages 1-27.

    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:eee:stapro:v:82:y:2012:i:5:p:949-958. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.