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Uniform limit theorems for functions of order statistics

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  • Wozabal, Nancy

Abstract

We discuss uniform limit theorems for linear combinations of order statistics, when a family of weighting functions (or score functions) is involved. We also show an application of the results to derive asymptotic properties of coherent risk functionals.

Suggested Citation

  • Wozabal, Nancy, 2009. "Uniform limit theorems for functions of order statistics," Statistics & Probability Letters, Elsevier, vol. 79(12), pages 1450-1455, June.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:12:p:1450-1455
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    References listed on IDEAS

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    1. Vandewalle, B. & Beirlant, J., 2006. "On univariate extreme value statistics and the estimation of reinsurance premiums," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 441-459, June.
    2. Bruce Jones & Ričardas Zitikis, 2003. "Empirical Estimation of Risk Measures and Related Quantities," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(4), pages 44-54.
    3. Robert Jarrow, 2002. "Put Option Premiums and Coherent Risk Measures," Mathematical Finance, Wiley Blackwell, vol. 12(2), pages 135-142, April.
    4. Jones, Bruce L. & Zitikis, Ricardas, 2007. "Risk measures, distortion parameters, and their empirical estimation," Insurance: Mathematics and Economics, Elsevier, vol. 41(2), pages 279-297, September.
    5. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    6. Christian Gourieroux & Wei Liu, 2006. "Sensitivity Analysis of Distortion Risk Measures," Working Papers 2006-33, Center for Research in Economics and Statistics.
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