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On tail index estimation using a sample with missing observations

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  • 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
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    References listed on IDEAS

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    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Jonathan B. Hill, 2005. "On Tail Index Estimation for Dependent, Heterogenous Data," Econometrics 0505005, University Library of Munich, Germany, revised 24 Mar 2006.
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