Abstract
This paper presents new approaches for the estimation of the extreme value index in the framework of randomly censored samples, based on the ideas of Kaplan-Meier integration and the synthetic data approach of Leurgans (1987). These ideas are developed here in the heavy-tailed case, and lead to modifications of the Hill estimator, for which the consistency is proved under first order conditions. Simulations exhibit good performances of the two approaches, compared to the only existing adaptation of the Hill estimator in this context
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Beirlant, J., Dierckx, G., Guillou, A., Stǎricǎ, C.: On exponential representations of log spacings of order statisticsIn extremes, Vol. 5, pp 157–180 (2002)
Beirlant, J., Dierckx, G., Guillou, A., Fils-Villetard, A.: Estimation of the extreme value index and extreme quantiles under random censoring In extremes, Vol. 10, pp 151–174 (2007)
Beirlant, J., Guillou, A., Toulemonde, G.: Peaks-over-threshold modeling under random censoring. In Comm. Stat: Theory and Methods 39, 1158–1179 (2010)
Brahimi, B., Meraghni, D., Necir, A.: Asymptotic normality of the adapted Hill estimator to censored data. working paper (2013)
Caeiro, F., Gomes, M.I., Pestana, D.: Direct reduction of bias of the classical Hill estimator In revstat, Vol. 3/2, pp 113–136 (2005)
Chow, Y.S.: Probability theory independence, interchangeability, martingales. Springer (1997)
Csörgő, S.: Universal Gaussian approximations under random censorship. Ann. stat. 2(6), 2744–2778 (1996)
de Haan, L., Ferreira, A.: Extreme Value Theory : an Introduction. Springer (2006)
Delecroix, M., Lopez, O., Patilea, V.: Nonlinear censored regression using synthetic data. Scand. J. Stat. 35, 248–265 (2008)
Einmahl, J., Fils-Villetard, A., Guillou, A.: Statistics of extremes under random censoring In bernoulli, Vol. 14, pp 207–227 (2008)
Gill, R.: Large sample behaviour of the product-limit estimator on the whole line. Ann. stat. 11(1), 49–58 (1983)
Gomes, M.I., de Haan, L., Rodrigues, L.H.: Tail index estimation for heavy-tailed models: accommodation of bias in weighted log-excesses. J. R. Stat. Soc. B70(1), 31–52 (2008)
Gomes, M.I., Neves, M.M.: Estimation of the extreme value index for randomly censored dataBiometrical Letters, Vol. 48, pp 1–22 (2011)
Koul, H., Susarla, V., Van Ryzin, J.: Regression analysis with randomly right-censored data. Ann. stat. 9(6), 1276–1288 (1981)
Leurgans, S.: Linear models, random censoring and synthetic dataBiometrika, Vol. 74 , pp 301–309 (1987)
Stute, W.: The central limit theorem under random censorship, Vol. 23, pp 422–439 (1995)
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Worms, J., Worms, R. New estimators of the extreme value index under random right censoring, for heavy-tailed distributions. Extremes 17, 337–358 (2014). https://doi.org/10.1007/s10687-014-0189-6
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DOI: https://doi.org/10.1007/s10687-014-0189-6