A. Balkema and L. De-haan, Residual Life Time at Great Age, The Annals of Probability, vol.2, issue.5, pp.792-801, 1974.
DOI : 10.1214/aop/1176996548

F. Caeiro, M. I. Gomes, and D. Pestana, A note on the asymptotic variance at optimal levels of a biascorrected Hill estimator, Stat. Probab. Letters, vol.79, pp.295-303, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00504135

G. Ciuperca and C. Mercadier, Semi-parametric estimation for heavy tailed distributions, available on HAL archive, 2008.
DOI : 10.1007/s10687-009-0086-6
URL : https://hal.archives-ouvertes.fr/hal-00292587

J. Diebolt, A. Guillou, and I. Rached, Approximation of the distribution of excesses through a generalized probability-weighted moments method, Journal of Statistical Planning and Inference, vol.137, issue.3, pp.841-857, 2007.
DOI : 10.1016/j.jspi.2006.06.012
URL : https://hal.archives-ouvertes.fr/hal-00693666

J. Diebolt, A. Guillou, and R. Worms, Asymptotic behaviour of the probability-weighted moments and penultimate approximation, ESAIM: Probability and Statistics, vol.7, pp.217-236, 2003.
DOI : 10.1051/ps:2003010

J. Diebolt, A. Guillou, and I. Rached, Approximation of the distribution of excesses through a generalized probability-weighted moments method, Journal of Statistical Planning and Inference, vol.137, issue.3, pp.841-857, 2007.
DOI : 10.1016/j.jspi.2006.06.012
URL : https://hal.archives-ouvertes.fr/hal-00693666

H. Drees and E. Kaufmann, Selecting the optimal sample fraction in univariate extreme value estimation, Stochastic Processes and their Applications, vol.75, issue.2, pp.149-172, 1998.
DOI : 10.1016/S0304-4149(98)00017-9

M. I. Fraga-alves, L. De-haan, and T. Lin, Estimation of the parameter controlling the speed of convergence in extreme value theory, Math. Methods of Statistics, vol.12, issue.2, pp.155-176, 2003.

M. I. Fraga-alves, L. De-haan, and T. Lin, Third order extended regular variation, pp.109-120, 2006.

M. I. Fraga-alves, M. I. Gomes, and L. De-haan, A new class of semi-parametric estimators of the second order parameter, Portugaliae Mathematica, vol.60, issue.2, pp.193-213, 2003.

M. I. Fraga-alves, M. I. Gomes, L. De-haan, and C. Neves, A note on second order conditions in extreme value theory: linking general and heavy tail conditions, REVSTAT Statistical Journal, vol.5, issue.3, p.285304, 2007.

M. I. Gomes, L. De-haan, and L. Peng, Semi-parametric estimation of the second order parameter in statistics of extremes, pp.387-414, 2002.

M. I. Gomes and J. Martins, Asymptotically unbiased " estimators of the tail index based on external estimation of the second order parameter, pp.5-31, 2002.

P. Hall and A. H. Welsh, Adaptive Estimates of Parameters of Regular Variation, The Annals of Statistics, vol.13, issue.1, pp.331-341, 1985.
DOI : 10.1214/aos/1176346596

J. Hosking and J. Wallis, Parameter and Quantile Estimation for the Generalized Pareto Distribution, Technometrics, vol.4, issue.3, pp.339-349, 1987.
DOI : 10.1016/0022-1694(85)90108-8

L. Peng, Asymptotically unbiased estimators for the extreme-value index, Statistics & Probability Letters, vol.38, issue.2, pp.107-115, 1998.
DOI : 10.1016/S0167-7152(97)00160-0

J. P. Raoult and R. Worms, Rate of convergence for the generalized Pareto approximation of the excesses, Advances in Applied Probability, vol.35, issue.04, pp.1007-1027, 2003.
DOI : 10.2307/1427562
URL : https://hal.archives-ouvertes.fr/hal-00693464

R. J. Serfling, Approximation Theorems of Mathematical Statistics, 1980.

A. W. Van and . Vaart, Asymptotic Statistics, Cambridge Series in Statistical and Probabilistic Mathematics, 2000.

R. Worms, Penultimate approximation for the distribution of the excesses, ESAIM: Probability and Statistics, vol.6, pp.21-31, 2002.
DOI : 10.1051/ps:2002002