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Edgeworth expansion for an estimator of the adjustment coefficient

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  • Brito, Margarida
  • Freitas, Ana Cristina Moreira

Abstract

We establish an Edgeworth expansion for an estimator of the adjustment coefficient R, directly related to the geometric-type estimator for general exponential tail coefficients, proposed in [Brito, M., Freitas, A.C.M., 2003. Limiting behaviour of a geometric-type estimator for tail indices. Insurance Math. Econom. 33, 211-226].Using the first term of the expansion, we construct improved confidence bounds for R. The accuracy of the approximation is illustrated using an example from insurance (cf. [Schultze, J., Steinebach, J., 1996. On least squares estimates of an exponential tail coefficient. Statist. Dec. 14, 353-372]).

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:43:y:2008:i:2:p:203-208
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Csorgo, Miklos & Steinebach, Josef, 1991. "On the estimation of the adjustment coefficient in risk theory via intermediate order statistics," Insurance: Mathematics and Economics, Elsevier, vol. 10(1), pages 37-50, March.
    4. 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.
    5. 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.
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